{"id":4812,"date":"2026-05-04T08:26:19","date_gmt":"2026-05-04T08:26:19","guid":{"rendered":"https:\/\/pausemaths.fr\/?p=4812"},"modified":"2026-05-05T07:33:31","modified_gmt":"2026-05-05T07:33:31","slug":"simple-distributivite-2","status":"publish","type":"post","link":"https:\/\/pausemaths.fr\/index.php\/2026\/05\/04\/simple-distributivite-2\/","title":{"rendered":"La simple distributivit\u00e9"},"content":{"rendered":"\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-794e3cfa wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"border-width:1px\">\n<p class=\"has-text-align-center wp-block-paragraph\">Facile<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column has-background is-layout-flow wp-block-column-is-layout-flow\" style=\"border-width:1px;background-color:#e637a3\">\n<p class=\"has-text-align-center wp-block-paragraph\">Moyen<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"border-width:1px\">\n<p class=\"has-text-align-center wp-block-paragraph\">Difficile<\/p>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-794e3cfa wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column has-background is-layout-flow wp-block-column-is-layout-flow\" style=\"border-width:1px;background-color:#f7aa1b\">\n<p class=\"has-text-align-center has-large-font-size wp-block-paragraph\"><strong>D\u00e9velopper <\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"border-width:1px\">\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>Factoriser<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-794e3cfa wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column has-background is-layout-flow wp-block-column-is-layout-flow\" style=\"border-width:1px;background-color:#5492f6\">\n<p class=\"has-text-align-center wp-block-paragraph\"><a href=\"https:\/\/pausemaths.fr\/index.php\/2026\/05\/04\/simple-distributivite-2\/\">Principe<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"border-width:1px\">\n<p class=\"has-text-align-center wp-block-paragraph\"><a href=\"https:\/\/pausemaths.fr\/index.php\/2026\/05\/04\/simple-distributivite-3\/\">Exercices corrig\u00e9s<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"border-width:1px\">\n<p class=\"has-text-align-center wp-block-paragraph\">A toi de jouer<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"border-width:1px\">\n<p class=\"has-text-align-center wp-block-paragraph\"><strong><a href=\"https:\/\/pausemaths.fr\/index.php\/2026\/04\/28\/simple-distributivite\/\">Maths Num\u00e9riques<\/a><\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator has-text-color has-contrast-color has-alpha-channel-opacity has-contrast-background-color has-background is-style-dots\"\/>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-794e3cfa wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-embed is-type-rich is-provider-prise-en-charge-des-contenus-embarqu-s wp-block-embed-prise-en-charge-des-contenus-embarqu-s wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Cours \u2666 Distributivit\u00e9 \u2022 D\u00e9velopper  k(a+b) = ka+kb et k(a-b) = ka - kb \u2666 Cinqui\u00e8me\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/KJtcmzKxfBc?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"border-width:1px;border-top-left-radius:20px;border-top-right-radius:20px;border-bottom-left-radius:20px;border-bottom-right-radius:20px;padding-top:var(--wp--preset--spacing--20);padding-right:var(--wp--preset--spacing--30);padding-bottom:var(--wp--preset--spacing--20);padding-left:var(--wp--preset--spacing--30);flex-basis:50%\">\n<p class=\"has-text-align-center has-x-large-font-size wp-block-paragraph\"><strong>Propri\u00e9t\u00e9s :<\/strong><\/p>\n\n\n\n<p class=\"has-large-font-size wp-block-paragraph\"><strong>Le produit d\u2019un nombre par une somme est \u00e9gal \u00e0 la somme des produits de ce nombre par chacun des termes de la somme :<\/strong><\/p>\n\n\n\n<center><big><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n  <mstyle mathcolor=\"red\">\n    <mi>k<\/mi>\n  <\/mstyle>\n  <mo>&#xD7;<\/mo>\n  <mo stretchy=\"false\">(<\/mo>\n  <mi>a<\/mi>\n  <mo>+<\/mo>\n  <mi>b<\/mi>\n  <mo stretchy=\"false\">)<\/mo>\n  <mo>=<\/mo>\n  <mstyle mathcolor=\"red\">\n    <mi>k<\/mi>\n  <\/mstyle>\n  <mo>&#xD7;<\/mo>\n  <mi>a<\/mi>\n  <mo>+<\/mo>\n  <mstyle mathcolor=\"red\">\n    <mi>k<\/mi>\n  <\/mstyle>\n  <mo>&#xD7;<\/mo>\n  <mi>b<\/mi>\n<\/math>\n<\/big><\/center>\n\n\n\n<p class=\"has-large-font-size wp-block-paragraph\">Le produit d\u2019un nombre par une diff\u00e9rence est \u00e9gal \u00e0 la diff\u00e9rence des produits de ce nombre par chacun des termes de la diff\u00e9rence :<\/p>\n\n\n\n<center><big><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n  <mstyle mathcolor=\"red\">\n    <mi>k<\/mi>\n  <\/mstyle>\n  <mo>&#xD7;<\/mo>\n  <mo stretchy=\"false\">(<\/mo>\n  <mi>a<\/mi>\n  <mo>&#x2212;<\/mo>\n  <mi>b<\/mi>\n  <mo stretchy=\"false\">)<\/mo>\n  <mo>=<\/mo>\n  <mstyle mathcolor=\"red\">\n    <mi>k<\/mi>\n  <\/mstyle>\n  <mo>&#xD7;<\/mo>\n  <mi>a<\/mi>\n  <mtext>&#xA0;<\/mtext>\n  <mo>&#x2212;<\/mo>\n  <mtext>&#xA0;<\/mtext>\n  <mstyle mathcolor=\"red\">\n    <mi>k<\/mi>\n  <\/mstyle>\n  <mo>&#xD7;<\/mo>\n  <mi>b<\/mi>\n<\/math>\n<\/center><\/big>\n<\/div>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator has-text-color has-contrast-color has-alpha-channel-opacity has-contrast-background-color has-background is-style-dots\"\/>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-794e3cfa wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><strong>Exemple 1  :<\/strong><br>La formule de calcul du p\u00e9rim\u00e8tre d&rsquo;un rectangle :<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\" style=\"margin-top:var(--wp--preset--spacing--20);margin-right:var(--wp--preset--spacing--20);margin-bottom:var(--wp--preset--spacing--20);margin-left:var(--wp--preset--spacing--20)\"><img loading=\"lazy\" decoding=\"async\" width=\"416\" height=\"251\" src=\"https:\/\/pausemaths.fr\/wp-content\/uploads\/2026\/05\/image-1.png\" alt=\"\" class=\"wp-image-4865\" srcset=\"https:\/\/pausemaths.fr\/wp-content\/uploads\/2026\/05\/image-1.png 416w, https:\/\/pausemaths.fr\/wp-content\/uploads\/2026\/05\/image-1-300x181.png 300w\" sizes=\"auto, (max-width: 416px) 100vw, 416px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><strong>Exemple 2 :<\/strong><\/p>\n\n\n\n<big>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n  <mi>A<\/mi>\n  <mo>=<\/mo>\n  <mn>3<\/mn>\n  <mstyle mathcolor=\"red\">\n    <mo>&#xD7;<\/mo>\n  <\/mstyle>\n  <mo stretchy=\"false\">(<\/mo>\n  <mn>6<\/mn>\n  <mstyle mathcolor=\"red\">\n    <mo>+<\/mo>\n  <\/mstyle>\n  <mi>x<\/mi>\n  <mo stretchy=\"false\">)<\/mo>\n<\/math>\n<br>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n  <mi>A<\/mi>\n  <mo>=<\/mo>\n  <mn>3<\/mn>\n  <mstyle mathcolor=\"red\">\n    <mo>&#xD7;<\/mo>\n  <\/mstyle>\n  <mn>6<\/mn>\n  <mstyle mathcolor=\"red\">\n    <mo>+<\/mo>\n  <\/mstyle>\n  <mn>3<\/mn>\n  <mstyle mathcolor=\"red\">\n    <mo>&#xD7;<\/mo>\n  <\/mstyle>\n  <mi>x<\/mi>\n<\/math>\n<br>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n  <mi>A<\/mi>\n  <mo>=<\/mo>\n  <mn>18<\/mn>\n  <mstyle mathcolor=\"red\">\n    <mo>+<\/mo>\n  <\/mstyle>\n  <mn>3<\/mn>\n  <mi>x<\/mi>\n<\/math>\n<\/big>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><strong>Exemple 3 :<\/strong><\/p>\n\n\n\n<big>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n  <mi>A<\/mi>\n  <mo>=<\/mo>\n  <mn>3<\/mn>\n  <mstyle mathcolor=\"red\">\n    <mo>&#xD7;<\/mo>\n  <\/mstyle>\n  <mo stretchy=\"false\">(<\/mo>\n  <mn>6<\/mn>\n  <mstyle mathcolor=\"red\">\n    <mo>&#x2212;<\/mo>\n  <\/mstyle>\n  <mi>x<\/mi>\n  <mo stretchy=\"false\">)<\/mo>\n<\/math>\n<br>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n  <mi>A<\/mi>\n  <mo>=<\/mo>\n  <mn>3<\/mn>\n  <mstyle mathcolor=\"red\">\n    <mo>&#xD7;<\/mo>\n  <\/mstyle>\n  <mn>6<\/mn>\n <mstyle mathcolor=\"red\">\n    <mo>&#x2212;<\/mo>\n  <\/mstyle>\n  <mn>3<\/mn>\n  <mstyle mathcolor=\"red\">\n    <mo>&#xD7;<\/mo>\n  <\/mstyle>\n  <mi>x<\/mi>\n<\/math>\n<br>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n  <mi>A<\/mi>\n  <mo>=<\/mo>\n  <mn>18<\/mn>\n  <mstyle mathcolor=\"red\">\n <mstyle mathcolor=\"red\">\n    <mo>&#x2212;<\/mo>\n  <\/mstyle>\n  <\/mstyle>\n  <mn>3<\/mn>\n  <mi>x<\/mi>\n<\/math>\n<\/big>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><strong>Exemple 4 :<\/strong><\/p>\n\n\n\n<big><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n  <mi>B<\/mi>\n  <mo>=<\/mo>\n  <mi>x<\/mi>\n  <mstyle mathcolor=\"red\">\n    <mo>&#xD7;<\/mo>\n  <\/mstyle>\n  <mo stretchy=\"false\">(<\/mo>\n  <mn>4<\/mn>\n <mstyle mathcolor=\"red\">\n    <mo>&#x2212;<\/mo>\n  <\/mstyle>\n  <mi>x<\/mi>\n  <mo stretchy=\"false\">)<\/mo>\n<\/math>\n<br>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n  <mi>B<\/mi>\n  <mo>=<\/mo>\n  <mi>x<\/mi>\n<mstyle mathcolor=\"red\">\n    <mo>&#xD7;<\/mo>\n  <\/mstyle>\n  <mn>4<\/mn>\n <mstyle mathcolor=\"red\">\n    <mo>&#x2212;<\/mo>\n  <\/mstyle>\n  <mi>x<\/mi>\n<mstyle mathcolor=\"red\">\n    <mo>&#xD7;<\/mo>\n  <\/mstyle>\n  <mi>x<\/mi>\n<\/math>\n<br>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n  <mi>B<\/mi>\n  <mo>=<\/mo>\n  <mn>4<\/mn>\n  <mi>x<\/mi>\n  <mstyle mathcolor=\"red\">\n    <mo>&#x2212;<\/mo>\n  <\/mstyle>\n  <msup>\n    <mi>x<\/mi>\n    <mrow data-mjx-texclass=\"ORD\">\n      <mn>2<\/mn>\n    <\/mrow>\n  <\/msup>\n<\/maths>  \n<\/big>\n<\/div>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator has-text-color has-contrast-color has-alpha-channel-opacity has-contrast-background-color has-background is-style-dots\"\/>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Source :<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><a href=\"https:\/\/college-willy-ronis.fr\/maths\/chapitre-3-la-simple-distributivite\/\">https:\/\/college-willy-ronis.fr\/maths\/chapitre-3-la-simple-distributivite\/<\/a><br><a href=\"http:\/\/mathematiques.daval.free.fr\/IMG\/pdf\/5_ch14_distributivite.pdf\">http:\/\/mathematiques.daval.free.fr\/IMG\/pdf\/5_ch14_distributivite.pdf<\/a><br><a href=\"https:\/\/gtzmaths.fr\/CL\/CoursDistributivite.html\">https:\/\/gtzmaths.fr\/CL\/CoursDistributivite.html<\/a><\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><a href=\"https:\/\/manuel.sesamath.net\/index.php?page=telechargement_4e_2011\">Exercice<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Facile Moyen Difficile D\u00e9velopper Factoriser Principe Exercices corrig\u00e9s A toi de jouer Maths Num\u00e9riques Propri\u00e9t\u00e9s : Le produit d\u2019un nombre par une somme est \u00e9gal \u00e0 la somme des produits de ce nombre par chacun des termes de la somme : k &#xD7; ( a + b ) = k &#xD7; a + k &#xD7; [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-4812","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/pausemaths.fr\/index.php\/wp-json\/wp\/v2\/posts\/4812","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pausemaths.fr\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pausemaths.fr\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pausemaths.fr\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/pausemaths.fr\/index.php\/wp-json\/wp\/v2\/comments?post=4812"}],"version-history":[{"count":48,"href":"https:\/\/pausemaths.fr\/index.php\/wp-json\/wp\/v2\/posts\/4812\/revisions"}],"predecessor-version":[{"id":4925,"href":"https:\/\/pausemaths.fr\/index.php\/wp-json\/wp\/v2\/posts\/4812\/revisions\/4925"}],"wp:attachment":[{"href":"https:\/\/pausemaths.fr\/index.php\/wp-json\/wp\/v2\/media?parent=4812"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pausemaths.fr\/index.php\/wp-json\/wp\/v2\/categories?post=4812"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pausemaths.fr\/index.php\/wp-json\/wp\/v2\/tags?post=4812"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}