{"id":18389,"date":"2024-10-23T18:19:26","date_gmt":"2024-10-23T16:19:26","guid":{"rendered":"http:\/\/localhost\/maths2\/?p=17920"},"modified":"2024-10-28T07:31:08","modified_gmt":"2024-10-28T06:31:08","slug":"chapitre-2-developper-et-reduire-expression-litterale","status":"publish","type":"post","link":"https:\/\/college-willy-ronis.fr\/maths\/chapitre-2-developper-et-reduire-expression-litterale\/","title":{"rendered":"Chapitre 2 : d\u00e9velopper et r\u00e9duire une expression litt\u00e9rale"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"18389\" class=\"elementor elementor-18389\">\n\t\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-14cd6900 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"14cd6900\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;gradient&quot;,&quot;shape_divider_bottom&quot;:&quot;wave-brush&quot;}\">\n\t\t\t\t\t\t\t<div class=\"elementor-background-overlay\"><\/div>\n\t\t\t\t\t\t<div class=\"elementor-shape elementor-shape-bottom\" data-negative=\"false\">\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 283.5 27.8\" preserveAspectRatio=\"none\">\n\t<path class=\"elementor-shape-fill\" d=\"M283.5,9.7c0,0-7.3,4.3-14,4.6c-6.8,0.3-12.6,0-20.9-1.5c-11.3-2-33.1-10.1-44.7-5.7\ts-12.1,4.6-18,7.4c-6.6,3.2-20,9.6-36.6,9.3C131.6,23.5,99.5,7.2,86.3,8c-1.4,0.1-6.6,0.8-10.5,2c-3.8,1.2-9.4,3.8-17,4.7\tc-3.2,0.4-8.3,1.1-14.2,0.9c-1.5-0.1-6.3-0.4-12-1.6c-5.7-1.2-11-3.1-15.8-3.7C6.5,9.2,0,10.8,0,10.8V0h283.5V9.7z M260.8,11.3\tc-0.7-1-2-0.4-4.3-0.4c-2.3,0-6.1-1.2-5.8-1.1c0.3,0.1,3.1,1.5,6,1.9C259.7,12.2,261.4,12.3,260.8,11.3z 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d=\"M154.5,26.7c-0.1-0.1-4.6,0.3-7.2,0c-7.3-0.7-17-3.2-16.6-2.9c0.4,0.3,13.7,3.1,17,3.3\tC152.6,27.5,154.6,26.8,154.5,26.7z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M41.9,19.3c0,0,1.2-0.3,2.9-0.1c1.7,0.2,5.8,0.9,8.2,0.7c4.2-0.4,7.4-2.7,7-2.6\tc-0.4,0-4.3,2.2-8.6,1.9c-1.8-0.1-5.1-0.5-6.7-0.4S41.9,19.3,41.9,19.3z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M75.5,12.6c0.2,0.1,2-0.8,4.3-1.1c2.3-0.2,2.1-0.3,2.1-0.5c0-0.1-1.8-0.4-3.4,0\tC76.9,11.5,75.3,12.5,75.5,12.6z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M15.6,13.2c0-0.1,4.3,0,6.7,0.5c2.4,0.5,5,1.9,5,2c0,0.1-2.7-0.8-5.1-1.4\tC19.9,13.7,15.7,13.3,15.6,13.2z\"\/>\n<\/svg>\t\t<\/div>\n\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-7f52ee39\" data-id=\"7f52ee39\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-10cbbbfb elementor-widget elementor-widget-heading\" data-id=\"10cbbbfb\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Chapitre 2<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5b89bd02 elementor-widget elementor-widget-heading\" data-id=\"5b89bd02\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">D\u00e9velopper et r\u00e9duire une expression litt\u00e9rale<\/h1>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-425a8c74 elementor-widget elementor-widget-text-editor\" data-id=\"425a8c74\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-7b11ca57\" data-id=\"7b11ca57\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-9922104 elementor-widget elementor-widget-image\" data-id=\"9922104\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"300\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2022\/02\/me-contacter-300x300.png\" class=\"attachment-medium size-medium wp-image-10663\" alt=\"\" srcset=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2022\/02\/me-contacter-300x300.png 300w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2022\/02\/me-contacter-150x150.png 150w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2022\/02\/me-contacter-768x768.png 768w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2022\/02\/me-contacter.png 912w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-bd40fb8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"bd40fb8\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-88657b5\" data-id=\"88657b5\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d9fcdfd elementor-widget elementor-widget-spacer\" data-id=\"d9fcdfd\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-1437c84 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1437c84\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-a3808d3\" data-id=\"a3808d3\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0009422 elementor-widget elementor-widget-heading\" data-id=\"0009422\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Chapitre 2 : d\u00e9velopper et r\u00e9duire une expression litt\u00e9rale<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-250ccf3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"250ccf3\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-bda0f93\" data-id=\"bda0f93\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-99b1fbe elementor-widget elementor-widget-spacer\" data-id=\"99b1fbe\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-35d9ec2 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"35d9ec2\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-6d2f874\" data-id=\"6d2f874\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c9e89b2 elementor-widget elementor-widget-text-editor\" data-id=\"c9e89b2\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>D\u00e9velopper et r\u00e9duire permet :<\/p><ul><li>de prouver que deux expressions litt\u00e9rales sont \u00e9quivalentes ;<\/li><li>de d\u00e9montrer qu&rsquo;une propri\u00e9t\u00e9 est vraie.<\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b2f4ee9 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b2f4ee9\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-3d09697\" data-id=\"3d09697\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e7bf24d elementor-widget elementor-widget-spacer\" data-id=\"e7bf24d\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-09b97da elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"09b97da\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-012814a\" data-id=\"012814a\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-08844c0 elementor-widget elementor-widget-heading\" data-id=\"08844c0\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">A) D\u00e9velopper avec la distributivit\u00e9 <\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6289888 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6289888\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-046d9c9\" data-id=\"046d9c9\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-81d92bc elementor-widget elementor-widget-text-editor\" data-id=\"81d92bc\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Propri\u00e9t\u00e9s : <\/strong>$k,a,b,c$ et $d$ sont des nombres relatifs quelconques :<\/p><p>\\begin{eqnarray*}<br \/>k \\times (a+b)&amp;=&amp;k\\times a + k\\times b \\\\<br \/>&amp;&amp;\\\\<br \/>(a+b)\\times (c+d)&amp;=&amp;a\\times c + a\\times d + b\\times c + b\\times d\\\\<br \/>\\end{eqnarray*}<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-1e708eb elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1e708eb\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-3b115e3\" data-id=\"3b115e3\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5185d4e elementor-widget elementor-widget-text-editor\" data-id=\"5185d4e\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Interpr\u00e9tation g\u00e9om\u00e9trique :<\/strong><\/p><p>\u00a0<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-18455 size-full\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/10\/double-distributivite.png\" alt=\"\" width=\"647\" height=\"204\" srcset=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/10\/double-distributivite.png 647w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/10\/double-distributivite-300x95.png 300w\" sizes=\"auto, (max-width: 647px) 100vw, 647px\" \/><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-018ccb3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"018ccb3\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-3a65beb\" data-id=\"3a65beb\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1b30929 elementor-widget elementor-widget-text-editor\" data-id=\"1b30929\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>\\begin{eqnarray*}<br \/>A&amp;=&amp;-3x(4x-6)\\\\<br \/>A&amp;=&amp;-12x^{2}+18x\\\\<br \/>\\end{eqnarray*}<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-62e886b\" data-id=\"62e886b\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-9cf8897 elementor-widget elementor-widget-image\" data-id=\"9cf8897\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"198\" height=\"73\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/10\/double-distributivite-2.png\" class=\"attachment-large size-large wp-image-18456\" alt=\"\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-f6bcd49 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f6bcd49\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-669880c\" data-id=\"669880c\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-fbcc72f elementor-widget elementor-widget-text-editor\" data-id=\"fbcc72f\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\\begin{eqnarray*}\nB&#038;=&#038;(2x-5)(3x-4)\\\\\nB&#038;=&#038;6x^{2}-8x-15x+20\\\\\nB&#038;=&#038;6x^{2}-23x+20\\\\\n\\end{eqnarray*}\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-dbc19c9\" data-id=\"dbc19c9\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1049de4 elementor-widget elementor-widget-image\" data-id=\"1049de4\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"189\" height=\"101\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/10\/double-distributivite-3.png\" class=\"attachment-large size-large wp-image-18457\" alt=\"\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2e6e5b4 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2e6e5b4\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-6fe41bb\" data-id=\"6fe41bb\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-353a9cf elementor-widget elementor-widget-video\" data-id=\"353a9cf\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/xoYaVMjGch4?si=rHLjRuslR60OVC-Q&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-8b9acf9 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8b9acf9\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-cb4f49b\" data-id=\"cb4f49b\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8dd4d10 elementor-widget elementor-widget-video\" data-id=\"8dd4d10\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/eseJGWUOvwc?si=R286uFJzMjZyd2El&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-419d638 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"419d638\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7536e37\" data-id=\"7536e37\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c7d179e elementor-widget elementor-widget-spacer\" data-id=\"c7d179e\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-580c231 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"580c231\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-fcc8f96\" data-id=\"fcc8f96\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f22a12a elementor-widget elementor-widget-heading\" data-id=\"f22a12a\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">B) D\u00e9velopper avec les identit\u00e9s remarquables<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ba80439 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ba80439\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7fffa08\" data-id=\"7fffa08\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5b9dcd3 elementor-widget elementor-widget-text-editor\" data-id=\"5b9dcd3\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Propri\u00e9t\u00e9s :<\/strong> $a$ et $b$ d\u00e9signent des nombres relatifs :<\/p><ul><li>$ (a+b)^{2}=a^{2}+2\\times a\\times b+b^{2}=a^{2}+2ab+b^{2}$<\/li><li>$ (a-b)^{2}=a^{2}-2\\times a\\times b+b^{2}=a^{2}-2ab+b^{2}$<\/li><li>$ (a+b)(a-b)=a^{2}-b^{2} $<\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-a2bacff elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a2bacff\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-c07c87b\" data-id=\"c07c87b\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a7c80d8 elementor-widget elementor-widget-text-editor\" data-id=\"a7c80d8\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Interpr\u00e9tation g\u00e9om\u00e9trique :<\/strong> Pour calculer l&rsquo;aire du carr\u00e9, on peut proc\u00e9der de deux mani\u00e8res :<\/p><ul><li>$A=(a+b)(a+b)=(a+b)^{2}$<\/li><li>$A=a^{2}+ab+ab+b^{2}=a^{2}+2ab+b^{2}$<\/li><\/ul><p>On en a d\u00e9duit : $(a+b)^{2}=a^{2}+2ab+b^{2}$.<\/p><p>\u00a0<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-18463 size-full\" src=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/10\/identites-remarquables.png\" alt=\"\" width=\"393\" height=\"339\" srcset=\"https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/10\/identites-remarquables.png 393w, https:\/\/college-willy-ronis.fr\/maths\/wp-content\/uploads\/2024\/10\/identites-remarquables-300x259.png 300w\" sizes=\"auto, (max-width: 393px) 100vw, 393px\" \/><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6424b1e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6424b1e\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-fee3e42\" data-id=\"fee3e42\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ddfba48 elementor-widget elementor-widget-text-editor\" data-id=\"ddfba48\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>D\u00e9monstration :<\/strong> D\u00e9montrons la premi\u00e8re identit\u00e9 remarquable :<br \/>\\begin{eqnarray*}<br \/>(a+b)^{2}&amp;=&amp;(a+b)(a+b)\\\\<br \/>&amp;=&amp;a\\times a+a\\times b+b\\times a+b\\times b\\\\<br \/>&amp;=&amp;a^{2}+a\\times b+a\\times b+b^{2}\\\\<br \/>&amp;=&amp;a^{2}+2\\times a\\times b+b^{2}\\\\<br \/>&amp;=&amp;a^{2}+2ab+b^{2}<br \/>\\end{eqnarray*}<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-22560d3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"22560d3\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4e4dec1\" data-id=\"4e4dec1\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b82553a elementor-widget elementor-widget-text-editor\" data-id=\"b82553a\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Exemples :<\/strong> Les identit\u00e9s remarquables permettent de d\u00e9velopper plus rapidement une expression :<br \/>\\begin{eqnarray*}<br \/>A&amp;=&amp;(2x+5)^{2}\\\\<br \/>A&amp;=&amp;(2x)^{2}+2\\times 2x\\times 5+5^{2}\\\\<br \/>A&amp;=&amp;4x^{2}+20x+25\\\\<br \/>\\end{eqnarray*}<\/p><p><br \/>\\begin{eqnarray*}<br \/>B&amp;=&amp;(x-6)^{2}\\\\<br \/>B&amp;=&amp;x^{2}-2\\times x\\times 6+6^{2}\\\\<br \/>B&amp;=&amp;x^{2}-12x+36\\\\<br \/>\\end{eqnarray*}<\/p><p><br \/>\\begin{eqnarray*}<br \/>C&amp;=&amp;(3x-4)(3x+4)\\\\<br \/>C&amp;=&amp;(3x)^{2}-4^{2}\\\\<br \/>C&amp;=&amp;9x^{2}-16<br \/>\\end{eqnarray*}<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-559fe99 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"559fe99\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-f9e4e01\" data-id=\"f9e4e01\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-dff13b9 elementor-widget elementor-widget-video\" data-id=\"dff13b9\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/mOwDaZ9GRRI?si=ILz8uudGuAYxT6r0&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2da1786 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2da1786\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-e820d46\" data-id=\"e820d46\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f8807a7 elementor-widget elementor-widget-text-editor\" data-id=\"f8807a7\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Exemples :<\/strong> Les identit\u00e9s remarquables peuvent servir pour calculer mentalement :<\/p><ul><li>$99\\times 101=(100-1)(100+1)=100^{2}-1^{2}=10~000-1=9~999$<\/li><li>$29^{2}=(30-1)^{2}=30^{2}-2\\times 30\\times 1<br \/>+1^{2}=900-60+1=841$<\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-be79a83 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"be79a83\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-ffc51ba\" data-id=\"ffc51ba\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3c7907e elementor-widget elementor-widget-video\" data-id=\"3c7907e\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/AThOZgY_AVY?si=jRBCQkGxhS0V_tmr&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-d69fc86 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d69fc86\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-af89dec\" data-id=\"af89dec\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-892061e elementor-widget elementor-widget-spacer\" data-id=\"892061e\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-becf20c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"becf20c\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-decaadf\" data-id=\"decaadf\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-38ae4cb elementor-widget elementor-widget-heading\" data-id=\"38ae4cb\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">C) Le calcul litt\u00e9ral pour d\u00e9montrer<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-1f2faf7 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1f2faf7\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-ecc893d\" data-id=\"ecc893d\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5cd1db5 elementor-widget elementor-widget-text-editor\" data-id=\"5cd1db5\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\tUne expression litt\u00e9rale peut traduire un programme de calcul. Cela permet de justifier que des programmes de calcul sont \u00e9quivalents.\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6c7f2a5 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6c7f2a5\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-688c876\" data-id=\"688c876\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7e186ec elementor-widget elementor-widget-text-editor\" data-id=\"7e186ec\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Exemple :<\/strong> Les programmes de calcul ci-dessous sont-ils \u00e9quivalents ?<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2e96519 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2e96519\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-e03fd3c\" data-id=\"e03fd3c\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f501bfb elementor-widget elementor-widget-text-editor\" data-id=\"f501bfb\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<ul><li>Choisir un nombre<\/li><li>Ajouter 7<\/li><li>Ajouter le nombre de d\u00e9part<\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-3afc3fe\" data-id=\"3afc3fe\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-846d852 elementor-widget elementor-widget-text-editor\" data-id=\"846d852\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<ul><li>Choisir un nombre<\/li><li>Multiplier le r\u00e9sultat par 2<\/li><li>Ajouter 10<\/li><li>Retrancher 3<\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-e975f84 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e975f84\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-5ab96a1\" data-id=\"5ab96a1\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b5592a3 elementor-widget elementor-widget-text-editor\" data-id=\"b5592a3\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Choisissons $x$ pour remplacer le nombre de d\u00e9part :<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b09e59c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b09e59c\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-3f047e2\" data-id=\"3f047e2\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-abbd5c1 elementor-widget elementor-widget-text-editor\" data-id=\"abbd5c1\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<ul><li>$x$<\/li><li>$x+7$<\/li><li>$x+7+x=2x+7$<\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-9b4e367\" data-id=\"9b4e367\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-da3ae7c elementor-widget elementor-widget-text-editor\" data-id=\"da3ae7c\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<ul><li>$x$<\/li><li>$2\\times x$<\/li><li>$2\\times x+10$<\/li><li>$2\\times x+10-3=2x+7$<\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-d8c2c77 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d8c2c77\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-0dd6923\" data-id=\"0dd6923\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f53b112 elementor-widget elementor-widget-text-editor\" data-id=\"f53b112\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\tLe r\u00e9sultat de ces deux programmes est donc identique pour n&rsquo;importe quelle valeur de $x$. Donc ces deux programmes de calcul sont \u00e9quivalents.\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-d5842e0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d5842e0\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-66353b2\" data-id=\"66353b2\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-82759c6 elementor-widget elementor-widget-text-editor\" data-id=\"82759c6\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\tUne expression litt\u00e9rale permet aussi de d\u00e9crire une propri\u00e9t\u00e9 g\u00e9n\u00e9rale de nombres.\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-f56404b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f56404b\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-dcd29a0\" data-id=\"dcd29a0\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3cd2b9d elementor-widget elementor-widget-text-editor\" data-id=\"3cd2b9d\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Exemples :<\/strong><\/p><ul><li>Si $n$ d\u00e9signe un nombre entier, on peut traduire la formulation \u00ab\u00a0\u00eatre la somme de deux entiers cons\u00e9cutifs\u00a0\u00bb par l&rsquo;expression litt\u00e9rale : $n+(n+1)$.<\/li><li>Si $n$ d\u00e9signe un nombre entier, on peut traduire la formulation \u00ab\u00a0\u00eatre un multiple de 3\u00a0\u00bb par l&rsquo;expression litt\u00e9rale : $3\\times n=3n$.<\/li><li>Si $n$ d\u00e9signe un nombre entier, on peut traduire la formulation \u00ab\u00a0\u00eatre un nombre pair\u00a0\u00bb par l&rsquo;expression litt\u00e9rale : $2\\times n=2n$.<\/li><li>Si $n$ d\u00e9signe un nombre entier, on peut traduire la formulation \u00ab\u00a0\u00eatre un nombre impair\u00a0\u00bb par l&rsquo;expression litt\u00e9rale : $2\\times n+1=2n+1$.<\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-23cf7ee elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"23cf7ee\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-ec76914\" data-id=\"ec76914\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8a08a09 elementor-widget elementor-widget-text-editor\" data-id=\"8a08a09\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\tLe calcul litt\u00e9ral permet de d\u00e9montrer qu&rsquo;une propri\u00e9t\u00e9 est vraie.\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-a153d41 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a153d41\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-c768ec8\" data-id=\"c768ec8\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6b31621 elementor-widget elementor-widget-text-editor\" data-id=\"6b31621\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Exemple :<\/strong> Montrer que pour n&rsquo;importe quel nombre entier $n$, $(n+1)^{2}-(n-1)^{2}$ est un multiple de 4.<\/p><p>\\begin{eqnarray*}<br \/>(n+1)^{2}-(n-1)^{2}&amp;=&amp;[n^{2}+2\\times n\\times 1+1^{2}]-[n^{2}-2\\times n\\times 1+1^{2}]\\\\<br \/>&amp;=&amp;[n^{2}+2n+1]-[n^{2}-2n+1]\\\\<br \/>&amp;=&amp;n^{2}+2n+1-n^{2}+2n-1\\\\<br \/>&amp;=&amp;4n<br \/>\\end{eqnarray*}<br \/>Donc pour tout nombre entier $n$, $(n+1)^{2}-(n-1)^{2}$ est bien un multiple de 4.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2081f5b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2081f5b\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4d30c7f\" data-id=\"4d30c7f\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a035fd9 elementor-widget elementor-widget-spacer\" data-id=\"a035fd9\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b61568e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b61568e\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-c2ed4a7\" data-id=\"c2ed4a7\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8120751 elementor-button-info elementor-align-center elementor-widget elementor-widget-button\" data-id=\"8120751\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-xl\" href=\"https:\/\/nuage02.apps.education.fr\/index.php\/s\/C3sc7R4fq3M7LHo\" target=\"_blank\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-icon elementor-align-icon-left\">\n\t\t\t\t<i aria-hidden=\"true\" class=\"far fa-arrow-alt-circle-right\"><\/i>\t\t\t<\/span>\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Exercices corrig\u00e9s<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-e0ca3f6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e0ca3f6\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-6d6cc4e\" data-id=\"6d6cc4e\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-24b0092 elementor-widget elementor-widget-spacer\" data-id=\"24b0092\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Chapitre 2 D\u00e9velopper et r\u00e9duire une expression litt\u00e9rale Chapitre 2 : d\u00e9velopper et r\u00e9duire une expression litt\u00e9rale D\u00e9velopper et r\u00e9duire permet : de prouver que deux expressions litt\u00e9rales sont \u00e9quivalentes ; de d\u00e9montrer qu&rsquo;une propri\u00e9t\u00e9 est vraie. A) D\u00e9velopper avec la distributivit\u00e9 Propri\u00e9t\u00e9s : $k,a,b,c$ et $d$ sont des nombres relatifs quelconques : begin{eqnarray*}k times [&hellip;]<\/p>\n","protected":false},"author":7440,"featured_media":18396,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"full-width-container","site-content-style":"unboxed","site-sidebar-style":"unboxed","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"disabled","ast-breadcrumbs-content":"","ast-featured-img":"disabled","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[43],"tags":[],"class_list":["post-18389","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cours-et-exercices-3eme"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v24.2 - 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