{"id":17399,"date":"2023-04-11T08:33:55","date_gmt":"2023-04-11T06:33:55","guid":{"rendered":"https:\/\/college-willy-ronis.fr\/maths\/?p=17399"},"modified":"2025-05-26T12:52:38","modified_gmt":"2025-05-26T10:52:38","slug":"chapitre-20-la-double-distributivite","status":"publish","type":"post","link":"https:\/\/college-willy-ronis.fr\/maths\/chapitre-20-la-double-distributivite\/","title":{"rendered":"Chapitre 20 : la double distributivit\u00e9"},"content":{"rendered":"\t\t
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Chapitre 20<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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La double distributivit\u00e9<\/h1>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Chapitre 20 : La double distributivit\u00e9<\/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
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Propri\u00e9t\u00e9 :<\/strong> $a$,$b$, $c$ et $d$ sont des nombres relatifs quelconques :
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\n\t\t\t\t\t\t\tD\u00e9monstration :<\/strong>\n$(a+b)(c+d)=(a+b)\\times c+(a+b)\\times d=a\\times c+b\\times c+a\\times d+b\\times d=a\\times c+a\\times d+b\\times c+b\\times d$\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
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Exemples :<\/strong>
\\begin{eqnarray*}
A&=&(3+2x)(x+4)\\\\
A&=&3\\times x+3\\times 4+2x\\times x+2x\\times 4\\\\
A&=&3x+12+2x^{2}+8x\\\\
A&=&2x^{2}+11x+12
\\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

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\n\t\t\t\t\t\t\t\\begin{eqnarray*}\nB&=&(2x-5)(3x-4)\\\\\nB&=&(2x+(-5))(3x+(-4))\\\\\nB&=&2x\\times 3x+2x\\times (-4)+(-5)\\times 3x+(-5)\\times (-4)\\\\\nB&=&6x^{2}+(-8x)+(-15x)+20\\\\\nB&=&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\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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Interpr\u00e9tation g\u00e9om\u00e9trique :<\/strong><\/p>

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Exemples :<\/strong> avec une r\u00e9daction permettant d’aller plus vite…\u00a0<\/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

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\\begin{eqnarray*}
B&=&(2x-5)(3x-4)\\\\
B&=&6x^{2}-8x-15x+20\\\\
B&=&6x^{2}-23x+20\\\\
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\"\"<\/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

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\\begin{eqnarray*}
C&=&(4x-7)(2x+6)-2(3x-4)\\\\
C&=&8x^{2}-14x+24x-42-6x+8\\\\
C&=&8x^{2}+4x-34\\\\
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\"\"<\/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

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\n\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t<\/i>\t\t\t<\/span>\n\t\t\t\t\t\tExercices 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
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Chapitre 20 La double distributivit\u00e9 Chapitre 20 : La double distributivit\u00e9 Propri\u00e9t\u00e9 : $a$,$b$, $c$ et $d$ sont des nombres relatifs quelconques : D\u00e9monstration : $(a+b)(c+d)=(a+b)times c+(a+b)times d=atimes c+btimes c+atimes d+btimes d=atimes c+atimes d+btimes c+btimes d$ Exemples :begin{eqnarray*}A&=&(3+2x)(x+4)\\A&=&3times x+3times 4+2xtimes x+2xtimes 4\\A&=&3x+12+2x^{2}+8x\\A&=&2x^{2}+11x+12end{eqnarray*} begin{eqnarray*} B&=&(2x-5)(3x-4)\\ B&=&(2x+(-5))(3x+(-4))\\ B&=&2xtimes 3x+2xtimes (-4)+(-5)times 3x+(-5)times (-4)\\ B&=&6x^{2}+(-8x)+(-15x)+20\\ B&=&6x^{2}-23x+20\\ end{eqnarray*}https:\/\/youtu.be\/V91qwpOZYXghttps:\/\/youtu.be\/esqOq7SdwNE Interpr\u00e9tation g\u00e9om\u00e9trique […]<\/p>\n","protected":false},"author":7440,"featured_media":17405,"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":"","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 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