{"id":164,"date":"2022-04-13T10:12:29","date_gmt":"2022-04-13T10:12:29","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=164"},"modified":"2025-01-21T09:38:32","modified_gmt":"2025-01-21T09:38:32","slug":"h-12-multiply-polynomials","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/h-12-multiply-polynomials\/","title":{"rendered":"H.12 Multiply polynomials"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color has-huge-font-size\" style=\"color:#00056d;text-transform:uppercase\"><strong> Multiply polynomials<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-04d9d6410ea0aa79bd5fd62d138d8458\" style=\"color:#74008b;text-transform:uppercase\">key notes:<\/p>\n\n\n\n<p class=\"has-large-font-size\">To&nbsp;simplify the product of two binomials, use the distributive&nbsp;property.<\/p>\n\n\n\n<p class=\"has-large-font-size\">As&nbsp;a shortcut, you can use the&nbsp;<strong>FOIL<\/strong>&nbsp;method. Find the products of the&nbsp;<strong>F<\/strong>irst,&nbsp;<strong>O<\/strong>utside,&nbsp;<strong>I<\/strong>nside,&nbsp;and&nbsp;<strong>L<\/strong>ast&nbsp;terms, and then add&nbsp;them.<\/p>\n\n\n\n<p class=\"has-large-font-size\">Square&nbsp;of a&nbsp;binomial:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>(a+b)<sup>2<\/sup>=a<sup>2<\/sup>+2ab+b<sup>2<\/sup><\/li>\n\n\n\n<li>(a\u2013b)<sup>2<\/sup>=a<sup>2<\/sup>\u20132ab+b<sup>2<\/sup><\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\">To&nbsp;multiply powers with the same base, add their&nbsp;exponents.<\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#9df6de\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-94b4a687efb4bed12fa2ee56d94e21f0\" style=\"color:#b00012\">\ud83d\udd14 Find&nbsp;the product. <\/p>\n\n\n\n<p>Simplify your&nbsp;answer.<\/p>\n\n\n\n<p>(u+4)(3u+3)<\/p>\n<\/div><\/div>\n\n\n\n<p>Use&nbsp;the distributive property to simplify&nbsp;(u+4)(3u+3).&nbsp;You can use the FOIL&nbsp;method:<\/p>\n\n\n\n<p>Multiply&nbsp;the first terms of&nbsp;(u+4)(<strong>3<\/strong>u+3):<\/p>\n\n\n\n<p>(u)(3u)=3u<sup>2<\/sup><\/p>\n\n\n\n<p>Multiply&nbsp;the outside terms of&nbsp;(u+4)(3u+<strong>3<\/strong>):<\/p>\n\n\n\n<p>(u)(3)=3u<\/p>\n\n\n\n<p>Multiply&nbsp;the inside terms of&nbsp;(u+<strong>4<\/strong>)(<strong>3<\/strong>u+3):<\/p>\n\n\n\n<p>(4)(3u)=12u<\/p>\n\n\n\n<p>Multiply&nbsp;the last terms of&nbsp;(u+<strong>4<\/strong>)(3u+<strong>3<\/strong>):<\/p>\n\n\n\n<p>(4)(3)=12<\/p>\n\n\n\n<p>Finally,&nbsp;add these results and&nbsp;simplify.<\/p>\n\n\n\n<p>3u<sup>2<\/sup>+3u+12u+12<\/p>\n\n\n\n<p>3u<sup>2<\/sup>+15u+12<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#bbb3f7\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-46ef44cc4511ad5d17912775a832c309\" style=\"color:#b00012\">\ud83d\udd14 Find&nbsp;the square.<\/p>\n\n\n\n<p> Simplify your&nbsp;answer.<\/p>\n\n\n\n<p>(3m\u20131)<sup>2<\/sup><\/p>\n<\/div><\/div>\n\n\n\n<p>(3m\u20131)<sup>2<\/sup>&nbsp;is the square of a binomial, just like&nbsp;(a\u2013b)<sup>2<\/sup>.&nbsp;So, you can find&nbsp;(3m\u20131)<sup>2<\/sup>&nbsp;with this&nbsp;formula:<\/p>\n\n\n\n<p>(a\u2013b)<sup>2<\/sup>=a<sup>2<\/sup>\u20132ab+b<sup>2<\/sup><\/p>\n\n\n\n<p>Replace&nbsp;a&nbsp;with&nbsp;3m&nbsp;and&nbsp;b&nbsp;with&nbsp;\u20131,&nbsp;then&nbsp;simplify.<\/p>\n\n\n\n<p>(<strong>3<\/strong>m\u2013<strong>1<\/strong>)<sup>2<\/sup><\/p>\n\n\n\n<p>(<strong>3<\/strong>m)<sup>2<\/sup>\u20132(<strong>3<\/strong>m)(<strong>1<\/strong>)+<strong>1<\/strong><sup>2<\/sup><\/p>\n\n\n\n<p>9m<sup>2<\/sup>\u20136m+1<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f0d889\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-857a24f20d0b64e379236cc4610157af\" style=\"color:#b00012\">\ud83d\udd14 Find&nbsp;the product.<\/p>\n\n\n\n<p> Simplify your&nbsp;answer.<\/p>\n\n\n\n<p>\u20133u<sup>2<\/sup>(3u<sup>2<\/sup>+2u)<\/p>\n<\/div><\/div>\n\n\n\n<p>Find&nbsp;the&nbsp;product.<\/p>\n\n\n\n<p>\u20133u<sup>2<\/sup>(3u<sup>2<\/sup>+2u)<\/p>\n\n\n\n<p>\u20133u<sup>2<\/sup>(3u<sup>2<\/sup>)+\u20133u<sup>2<\/sup>(2u)                   Apply&nbsp;the distributive&nbsp;property<\/p>\n\n\n\n<p>\u20139u<sup>4<\/sup>+\u20136u<sup>3<\/sup>                             Simplify<\/p>\n\n\n\n<p>\u20139u<sup>4<\/sup>\u20136u<sup>3<\/sup>                           Rewrite&nbsp;as&nbsp;subtraction<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">let&#8217;s practice!\ud83d\udd8a\ufe0f<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/85323\/499\/263\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-39.png\" alt=\"\" class=\"wp-image-6875\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-39.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-39-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-39-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/51800\/097\/149\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-57.png\" alt=\"\" class=\"wp-image-6876\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-57.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-57-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-57-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Multiply polynomials key notes: To&nbsp;simplify the product of two binomials, use the distributive&nbsp;property. As&nbsp;a shortcut, you can use the&nbsp;FOIL&nbsp;method. Find the products of the&nbsp;First,&nbsp;Outside,&nbsp;Inside,&nbsp;and&nbsp;Last&nbsp;terms, and then add&nbsp;them. Square&nbsp;of a&nbsp;binomial: To&nbsp;multiply powers with the same base, add their&nbsp;exponents. Learn with an example \ud83d\udd14 Find&nbsp;the product. Simplify your&nbsp;answer. (u+4)(3u+3) Use&nbsp;the distributive property to simplify&nbsp;(u+4)(3u+3).&nbsp;You can use the<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/h-12-multiply-polynomials\/\">Continue reading <span class=\"screen-reader-text\">&#8220;H.12 Multiply polynomials&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-164","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/164","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=164"}],"version-history":[{"count":11,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/164\/revisions"}],"predecessor-version":[{"id":17424,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/164\/revisions\/17424"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=164"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}