{"id":156,"date":"2022-04-13T10:11:10","date_gmt":"2022-04-13T10:11:10","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=156"},"modified":"2025-01-18T07:36:23","modified_gmt":"2025-01-18T07:36:23","slug":"h-8-multiply-a-polynomial-by-a-monomial","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/h-8-multiply-a-polynomial-by-a-monomial\/","title":{"rendered":"H.8 Multiply a polynomial by a monomial"},"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 a polynomial by a monomial<\/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<ol class=\"wp-block-list has-large-font-size\">\n<li><strong>Definition:<\/strong>\n<ul class=\"wp-block-list\">\n<li>A polynomial is an expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication.<\/li>\n\n\n\n<li>A monomial is a polynomial with only one term.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Multiplying a Monomial by a Polynomial:<\/strong>\n<ul class=\"wp-block-list\">\n<li>To multiply a monomial by a polynomial, distribute each term of the monomial to every term in the polynomial.<\/li>\n\n\n\n<li>Example: 3\ufffd\u22c5(2\ufffd2+5\ufffd\u22121)3<em>x<\/em>\u22c5(2<em>x<\/em>2+5<em>x<\/em>\u22121)\n<ul class=\"wp-block-list\">\n<li>Distribute 3x to each term: 3\ufffd\u22c52\ufffd2+3\ufffd\u22c55\ufffd\u22123\ufffd\u22c513<em>x<\/em>\u22c52<em>x<\/em>2+3<em>x<\/em>\u22c55<em>x<\/em>\u22123<em>x<\/em>\u22c51<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Multiplication Rules:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Multiply coefficients together.<\/li>\n\n\n\n<li>Add exponents when the base (variable) is the same.\n<ul class=\"wp-block-list\">\n<li>Example: 2\ufffd3\u22c54\ufffd2=8\ufffd3+2=8\ufffd52<em>x<\/em>3\u22c54<em>x<\/em>2=8<em>x<\/em>3+2=8<em>x<\/em>5<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Combining Like Terms:<\/strong>\n<ul class=\"wp-block-list\">\n<li>After multiplying, combine like terms by adding or subtracting coefficients.\n<ul class=\"wp-block-list\">\n<li>Example: 3\ufffd\u22c52\ufffd2+3\ufffd\u22c55\ufffd\u22123\ufffd\u22c513<em>x<\/em>\u22c52<em>x<\/em>2+3<em>x<\/em>\u22c55<em>x<\/em>\u22123<em>x<\/em>\u22c51\n<ul class=\"wp-block-list\">\n<li>Combine like terms: 6\ufffd3+15\ufffd2\u22123\ufffd6<em>x<\/em>3+15<em>x<\/em>2\u22123<em>x<\/em><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Be Mindful of Signs:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Pay attention to the signs when distributing the monomial.<\/li>\n\n\n\n<li>Example: (\u22122\ufffd)\u22c5(3\ufffd2\u22124\ufffd+1)(\u22122<em>y<\/em>)\u22c5(3<em>y<\/em>2\u22124<em>y<\/em>+1)\n<ul class=\"wp-block-list\">\n<li>Distribute \u22122\ufffd\u22122<em>y<\/em>: \u22122\ufffd\u22c53\ufffd2+(\u22122\ufffd)\u22c5(\u22124\ufffd)+(\u22122\ufffd)\u22c51\u22122<em>y<\/em>\u22c53<em>y<\/em>2+(\u22122<em>y<\/em>)\u22c5(\u22124<em>y<\/em>)+(\u22122<em>y<\/em>)\u22c51<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Practice with Examples:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Practice various examples to reinforce the concept.<\/li>\n\n\n\n<li>Example: 4\ufffd\u22c5(2\ufffd2\u22123\ufffd+1)4<em>a<\/em>\u22c5(2<em>a<\/em>2\u22123<em>a<\/em>+1)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Real-Life Applications:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Understanding how to multiply polynomials by monomials is useful in algebraic expressions and equations, which are common in various real-life scenarios.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Check Your Answers:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Always check your final answer by simplifying and ensuring it makes sense in the context of the problem.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Review Properties of Exponents:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Knowledge of exponent rules is essential for simplifying expressions when dealing with monomials and polynomials.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Challenge Problems:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Challenge yourself with more complex problems to deepen your understanding.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\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:#95e38d\"><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-c8f18047e9c872f64ab031af493260e7\" style=\"color:#b00012\">\u27a1\ufe0f Find&nbsp;the product. <\/p>\n\n\n\n<p>Simplify your&nbsp;answer<\/p>\n\n\n\n<p>r.\u20133(\u2013q<sup>2<\/sup> + 2)<\/p>\n<\/div><\/div>\n\n\n\n<p>Find&nbsp;the&nbsp;product.<\/p>\n\n\n\n<p>\u20133 (\u2013q<sup>2 <\/sup>+ 2)<\/p>\n\n\n\n<p>\u20133 (\u2013q<sup>2<\/sup>) + \u20133(2)              Apply&nbsp;the distributive&nbsp;property<\/p>\n\n\n\n<p>3q<sup>2<\/sup>+\u20136                        Simplify<\/p>\n\n\n\n<p>3q<sup>2<\/sup>\u20136                        Rewrite&nbsp;as&nbsp;subtraction<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#a099e9\"><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>\u27a1\ufe0f Find&nbsp;the product. <\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-a9e5420f42b9eec6fc7520fa5866c16c\" style=\"color:#b00012\">Simplify your&nbsp;answer.<\/p>\n\n\n\n<p>\u20139(2z<sup>2<\/sup>\u20137)<\/p>\n<\/div><\/div>\n\n\n\n<p>Find&nbsp;the&nbsp;product.<\/p>\n\n\n\n<p>\u20139(2z<sup>2<\/sup>\u20137)<\/p>\n\n\n\n<p>\u20139(2z<sup>2<\/sup>+\u20137)               Rewrite&nbsp;as&nbsp;addition<\/p>\n\n\n\n<p>\u20139(2z<sup>2<\/sup>)+\u20139(\u20137)      Apply&nbsp;the distributive&nbsp;property<\/p>\n\n\n\n<p>\u201318z<sup>2<\/sup>+63            Simplify<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#eed893\"><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>\u27a1\ufe0f Find&nbsp;the product.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-6ac0e9da8b677b7db359fff7931bb58f\" style=\"color:#b00012\"> Simplify your&nbsp;answer.<\/p>\n\n\n\n<p>\u20133k (k<sup>2<\/sup>\u20134k)<\/p>\n<\/div><\/div>\n\n\n\n<p>Find&nbsp;the&nbsp;product. <\/p>\n\n\n\n<p>\u20133k (k<sup>2<\/sup>\u20134k)<\/p>\n\n\n\n<p>\u20133k (k<sup>2<\/sup>+\u20134k)                       Rewrite&nbsp;as&nbsp;addition<\/p>\n\n\n\n<p>\u20133k (k<sup>2<\/sup>) + \u20133k (\u20134k)        Apply&nbsp;the distributive&nbsp;property<\/p>\n\n\n\n<p>\u2013 3k<sup>3<\/sup>+12k<sup>2 <\/sup>           Simplify<\/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\/85169\/666\/622\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-35.png\" alt=\"\" class=\"wp-image-6852\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-35.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-35-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-35-150x150.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\/51761\/958\/333\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-53.png\" alt=\"\" class=\"wp-image-6853\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-53.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-53-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-53-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Multiply a polynomial by a monomial key notes: Learn with an example \u27a1\ufe0f Find&nbsp;the product. Simplify your&nbsp;answer r.\u20133(\u2013q2 + 2) Find&nbsp;the&nbsp;product. \u20133 (\u2013q2 + 2) \u20133 (\u2013q2) + \u20133(2) Apply&nbsp;the distributive&nbsp;property 3q2+\u20136 Simplify 3q2\u20136 Rewrite&nbsp;as&nbsp;subtraction \u27a1\ufe0f Find&nbsp;the product. Simplify your&nbsp;answer. \u20139(2z2\u20137) Find&nbsp;the&nbsp;product. \u20139(2z2\u20137) \u20139(2z2+\u20137) Rewrite&nbsp;as&nbsp;addition \u20139(2z2)+\u20139(\u20137) Apply&nbsp;the distributive&nbsp;property \u201318z2+63 Simplify \u27a1\ufe0f Find&nbsp;the product. Simplify your&nbsp;answer.<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/h-8-multiply-a-polynomial-by-a-monomial\/\">Continue reading <span class=\"screen-reader-text\">&#8220;H.8 Multiply a polynomial by a monomial&#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-156","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/156","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=156"}],"version-history":[{"count":13,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/156\/revisions"}],"predecessor-version":[{"id":17420,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/156\/revisions\/17420"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=156"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}