{"id":503,"date":"2022-04-13T05:22:50","date_gmt":"2022-04-13T05:22:50","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=503"},"modified":"2025-02-23T06:55:44","modified_gmt":"2025-02-23T06:55:44","slug":"y-7-factorise-by-grouping","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/y-7-factorise-by-grouping\/","title":{"rendered":"Y.7 Factorise by grouping"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Factorise by grouping<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-4d4696560822e7cb72ec4be90d4370b1\" style=\"color:#74008b\">Key Notes:<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-00e2cf6c9fd8c5b98a80e94368c8461b\" style=\"color:#000060\"><strong>Understanding Grouping<\/strong>: <\/p>\n\n\n\n<p class=\"has-large-font-size\">Factorising by grouping is a technique used when there are four terms in an algebraic expression.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-488fd2c15e07c2eac8388d85466d5c52\" style=\"color:#000060\"><strong>Identifying Common Factors<\/strong>: <\/p>\n\n\n\n<p class=\"has-large-font-size\">Look for common factors between pairs of terms within the expression.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-519e1fc58304c514fa1540a241132a9d\" style=\"color:#000060\"><strong>Grouping Strategy<\/strong>: <\/p>\n\n\n\n<p class=\"has-large-font-size\">Group the terms in pairs where each pair shares a common factor.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-d088359cd97529b840d8e176631ad86d\" style=\"color:#000060\"><strong>Factorisation Process<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Factor out the common factor from each pair of terms.<\/li>\n\n\n\n<li>This usually results in two groups, each with a common factor.<\/li>\n\n\n\n<li>Factor out the common factor that remains between the two groups.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>Example<\/strong>: Consider an expression like ax + ay + bx + by:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Grouping terms gives us (ax + ay) + (bx + by).<\/li>\n\n\n\n<li>Factor out a from the first group: a(x + y).<\/li>\n\n\n\n<li>Factor out b from the second group: b(x + y).<\/li>\n\n\n\n<li>Finally, factor out (x + y) from a(x + y) + b(x + y) to get (a + b)(x + y).<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-text-color has-link-color has-large-font-size wp-elements-3fefd20f8ce119a518e5f53333ab5486\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#f5abea\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\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-d4458458b1050fc62cfedb652616a89f\" style=\"color:#b00012\">\ud83c\udfba <strong>Factor.<\/strong><\/p>\n\n\n\n<p>4r<sup>3<\/sup> \u2013 8r<sup>2<\/sup> + 9r \u2013 18 =_____<\/p>\n<\/div><\/div>\n\n\n\n<p>Factor&nbsp;by&nbsp;grouping.<\/p>\n\n\n\n<p>4r<sup>3<\/sup> \u2013 8r<sup>2 <\/sup>+ 9r \u2013 18<\/p>\n\n\n\n<p><strong>4<\/strong>r<strong><sup>2<\/sup><\/strong>(r \u2013 <strong>2<\/strong>) + <strong>9<\/strong>(r \u2013 <strong>2<\/strong>) Factor&nbsp;by grouping; the expressions in brackets should&nbsp;match<\/p>\n\n\n\n<p>(<strong>4<\/strong>r<strong><sup>2<\/sup><\/strong> + <strong>9<\/strong>)(r \u2013 <strong>2<\/strong>)Apply&nbsp;the distributive&nbsp;property<\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#a6f3b7\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\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-ab7cfc42ea49f8856263d62ff6943cea\" style=\"color:#b00012\">\ud83c\udfba<strong> Factor.<\/strong><\/p>\n\n\n\n<p>9x<sup>3<\/sup> \u2013 9x<sup>2<\/sup> + 5x \u2013 5 =____<\/p>\n<\/div><\/div>\n\n\n\n<p>Factor&nbsp;by&nbsp;grouping.<\/p>\n\n\n\n<p>9x<sup>3<\/sup> \u2013 9x<sup>2<\/sup> + 5x \u2013 5<\/p>\n\n\n\n<p><strong>9<\/strong>x<strong><sup>2<\/sup><\/strong>(x \u2013 <strong>1<\/strong>) + <strong>5<\/strong>(x \u2013 <strong>1<\/strong>) Factor&nbsp;by grouping; the expressions in brackets should&nbsp;match<\/p>\n\n\n\n<p>(<strong>9<\/strong>x<strong><sup>2<\/sup><\/strong> + <strong>5<\/strong>)(x \u2013 <strong>1<\/strong>) Apply&nbsp;the distributive&nbsp;property<\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#f7f699\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\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-ab7cfc42ea49f8856263d62ff6943cea\" style=\"color:#b00012\">\ud83c\udfba<strong> Factor.<\/strong><\/p>\n\n\n\n<p>14x<sup>3<\/sup> \u2013 7x<sup>2<\/sup> + 2x \u2013 1=_____<\/p>\n<\/div><\/div>\n\n\n\n<p>Factor&nbsp;by&nbsp;grouping.<\/p>\n\n\n\n<p>14x<sup>3<\/sup> \u2013 7x<sup>2<\/sup> + 2x \u2013 1<\/p>\n\n\n\n<p><strong>7<\/strong>x<strong><sup>2<\/sup><\/strong>(<strong>2<\/strong>x \u2013 <strong>1<\/strong>) + <strong>1<\/strong>(<strong>2<\/strong>x \u2013 <strong>1<\/strong>)Factor&nbsp;by grouping; the expressions in brackets should&nbsp;match<\/p>\n\n\n\n<p>(<strong>7<\/strong>x<strong><sup>2<\/sup><\/strong> + <strong>1<\/strong>)(<strong>2<\/strong>x \u2013 <strong>1<\/strong>)Apply&nbsp;the distributive&nbsp;property<\/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!<\/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\/86522\/369\/339\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-165.png\" alt=\"\" class=\"wp-image-9022\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-165.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-165-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-165-150x150.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\/86300\/530\/388\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-170.png\" alt=\"\" class=\"wp-image-9024\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-170.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-170-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-170-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Factorise by grouping Key Notes: Understanding Grouping: Factorising by grouping is a technique used when there are four terms in an algebraic expression. Identifying Common Factors: Look for common factors between pairs of terms within the expression. Grouping Strategy: Group the terms in pairs where each pair shares a common factor. Factorisation Process: Example: Consider<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/y-7-factorise-by-grouping\/\">Continue reading <span class=\"screen-reader-text\">&#8220;Y.7 Factorise by grouping&#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-503","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_hostinger_reach_plugin_has_subscription_block":false,"_hostinger_reach_plugin_is_elementor":false,"_links":{"self":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/503","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=503"}],"version-history":[{"count":22,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/503\/revisions"}],"predecessor-version":[{"id":19948,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/503\/revisions\/19948"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=503"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}