{"id":148,"date":"2022-04-13T10:10:00","date_gmt":"2022-04-13T10:10:00","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=148"},"modified":"2025-01-17T12:01:05","modified_gmt":"2025-01-17T12:01:05","slug":"h-4-add-and-subtract-polynomials","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/h-4-add-and-subtract-polynomials\/","title":{"rendered":"H.4 Add and subtract 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> Add and subtract 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\"><strong>Polynomials:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">A polynomial is an algebraic expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication, but not division by a variable.<\/li>\n\n\n\n<li class=\"has-large-font-size\">Examples of polynomials: 3\ufffd2+2\ufffd\u221253<em>x<\/em>2+2<em>x<\/em>\u22125, 4\ufffd3\u22122\ufffd+74<em>y<\/em>3\u22122<em>y<\/em>+7.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>Like Terms:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">Terms are terms that have the same variable(s) raised to the same exponent(s).<\/li>\n\n\n\n<li class=\"has-large-font-size\">Example: 3\ufffd23<em>x<\/em>2 and 2\ufffd22<em>x<\/em>2 are like terms.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>Adding Polynomials:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">To add polynomials, combine like terms by adding or subtracting their coefficients.<\/li>\n\n\n\n<li class=\"has-large-font-size\">Example: (3\ufffd2+2\ufffd\u22125)+(4\ufffd2\u22127\ufffd+1)=7\ufffd2\u22125\ufffd\u22124(3<em>x<\/em>2+2<em>x<\/em>\u22125)+(4<em>x<\/em>2\u22127<em>x<\/em>+1)=7<em>x<\/em>2\u22125<em>x<\/em>\u22124.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>Subtracting Polynomials:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">To subtract polynomials, distribute the subtraction sign across each term in the second polynomial, then add.<\/li>\n\n\n\n<li class=\"has-large-font-size\">Example: (3\ufffd2+2\ufffd\u22125)\u2212(4\ufffd2\u22127\ufffd+1)=\u22121\ufffd2+9\ufffd\u22126(3<em>x<\/em>2+2<em>x<\/em>\u22125)\u2212(4<em>x<\/em>2\u22127<em>x<\/em>+1)=\u22121<em>x<\/em>2+9<em>x<\/em>\u22126.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>Be Careful with Signs:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">Pay attention to signs when combining or subtracting terms.<\/li>\n\n\n\n<li class=\"has-large-font-size\">Double-check signs in each step to avoid errors.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>Zero Pairs:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">When adding or subtracting, look for zero pairs (terms that cancel each other out).<\/li>\n\n\n\n<li class=\"has-large-font-size\">Example: 2\ufffd\u22122\ufffd=02<em>x<\/em>\u22122<em>x<\/em>=0, so these terms create a zero pair.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>Examples:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">(2\ufffd2+3\ufffd\u22121)+(4\ufffd2\u22122\ufffd+5)=6\ufffd2+\ufffd+4(2<em>x<\/em>2+3<em>x<\/em>\u22121)+(4<em>x<\/em>2\u22122<em>x<\/em>+5)=6<em>x<\/em>2+<em>x<\/em>+4<\/li>\n\n\n\n<li class=\"has-large-font-size\">(5\ufffd3+2\ufffd2\u22123\ufffd)\u2212(2\ufffd3\u2212\ufffd2+7\ufffd)=3\ufffd3+3\ufffd2\u221210\ufffd(5<em>y<\/em>3+2<em>y<\/em>2\u22123<em>y<\/em>)\u2212(2<em>y<\/em>3\u2212<em>y<\/em>2+7<em>y<\/em>)=3<em>y<\/em>3+3<em>y<\/em>2\u221210<em>y<\/em><\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>Practice:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">Practice adding and subtracting polynomials with various examples to reinforce understanding.<\/li>\n<\/ul>\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:#b3f4cc\"><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-e5e4676aa108c5f82ad9d25355b58b64\" style=\"color:#b00012\">\u27a1\ufe0f Subtract.<\/p>\n\n\n\n<p>(7b + 8) \u2013 (5b + 4)<\/p>\n<\/div><\/div>\n\n\n\n<p>Subtract.<\/p>\n\n\n\n<p>(7b + 8) \u2013 (5b + 4)<\/p>\n\n\n\n<p>(7b + 8) + (\u20135b \u2013 4)                       Rewrite&nbsp;as&nbsp;addition<\/p>\n\n\n\n<p>(7b + \u20135b) + (8 + \u20134)                 Group&nbsp;like&nbsp;terms<\/p>\n\n\n\n<p>2b + 4                                      Combine like terms<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#ecdaa3\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group\"><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-e5e4676aa108c5f82ad9d25355b58b64\" style=\"color:#b00012\">\u27a1\ufe0f Subtract.<\/p>\n\n\n\n<p>(5s<sup>2<\/sup> + 7s) \u2013 (4s<sup>2 <\/sup>+ 7s)<\/p>\n<\/div><\/div>\n\n\n\n<p>Subtract.<\/p>\n\n\n\n<p>(5s<sup>2<\/sup> + 7s) \u2013 (4s<sup>2 <\/sup> + 7s)<\/p>\n\n\n\n<p>(5s<sup>2<\/sup> + 7s) + (\u20134s<sup>2 <\/sup>\u2013 7s)               Rewrite&nbsp;as&nbsp;addition<\/p>\n\n\n\n<p>(5s<sup>2 <\/sup>+ \u20134s<sup>2<\/sup>) + (7s + \u20137s)         Group&nbsp;like&nbsp;terms<\/p>\n\n\n\n<p>1s<sup>2<\/sup> + 0s                               Combine&nbsp;like&nbsp;terms<\/p>\n<\/div><\/div>\n\n\n\n<p>s<sup>2<\/sup>                                    Simplify<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#afb8f0\"><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-e5e4676aa108c5f82ad9d25355b58b64\" style=\"color:#b00012\">\u27a1\ufe0f Subtract.<\/p>\n\n\n\n<p>(7d+5) \u2013 (3d + 3)<\/p>\n<\/div><\/div>\n\n\n\n<p>Subtract.<\/p>\n\n\n\n<p>(7d + 5) \u2013 (3d + 3)<\/p>\n\n\n\n<p>(7d + 5) + (\u20133d \u2013 3)                        Rewrite&nbsp;as&nbsp;addition<\/p>\n\n\n\n<p>(7d + \u20133d) + (5 + \u20133)                  Group&nbsp;like&nbsp;terms<\/p>\n\n\n\n<p>4d + 2                                    Combine like terms<\/p>\n<\/div><\/div>\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\/85132\/546\/977\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-31.png\" alt=\"\" class=\"wp-image-6830\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-31.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-31-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-31-150x150.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\/51760\/389\/185\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-49.png\" alt=\"\" class=\"wp-image-6831\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-49.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-49-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-49-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Add and subtract polynomials key notes: Polynomials: Like Terms: Adding Polynomials: Subtracting Polynomials: Be Careful with Signs: Zero Pairs: Examples: Practice: Learn with an example \u27a1\ufe0f Subtract. (7b + 8) \u2013 (5b + 4) Subtract. (7b + 8) \u2013 (5b + 4) (7b + 8) + (\u20135b \u2013 4) Rewrite&nbsp;as&nbsp;addition (7b + \u20135b) + (8<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/h-4-add-and-subtract-polynomials\/\">Continue reading <span class=\"screen-reader-text\">&#8220;H.4 Add and subtract 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-148","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/148","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=148"}],"version-history":[{"count":10,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/148\/revisions"}],"predecessor-version":[{"id":17413,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/148\/revisions\/17413"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=148"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}