{"id":454,"date":"2022-04-13T09:25:09","date_gmt":"2022-04-13T09:25:09","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=454"},"modified":"2024-01-06T09:24:20","modified_gmt":"2024-01-06T09:24:20","slug":"aa-5-factorise-quadratics-special-cases","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/aa-5-factorise-quadratics-special-cases\/","title":{"rendered":"AA.5 Factorise quadratics: special cases"},"content":{"rendered":"\n

Factorise quadratics: special cases<\/strong><\/h2>\n\n\n\n

key notes:<\/p>\n\n\n\n

\n

Factorizing\u00a0perfect square\u00a0trinomials:<\/p>\n\n\n\n

a2<\/sup>+2ab+b2<\/sup>=(a+b)2<\/sup><\/p>\n\n\n\n

a2<\/sup>\u20132ab+b2<\/sup>=(a\u2013b)2<\/sup><\/p>\n<\/div><\/div>\n\n\n\n

\n

Factorizing a difference of squares:<\/p>\n\n\n\n

a2<\/sup>\u2013b2<\/sup>=(a+b)(a\u2013b)<\/p>\n<\/div><\/div>\n\n\n\n

Learn with an example<\/strong><\/p>\n\n\n\n

\n
\n

\u27a1\ufe0f Factorise.<\/p>\n\n\n\n

25r2<\/sup>+20r+4<\/p>\n<\/div><\/div>\n\n\n\n

Notice that 25r2<\/sup>+20r+4 is a perfect square trinomial because it can be written in the form a2<\/sup>+2ab+b2, where a is 5r and b is 2.<\/p>\n\n\n\n

a2<\/sup>+2ab+b2<\/sup><\/p>\n\n\n\n

(5r)2<\/sup>+25r2+22<\/sup><\/p>\n\n\n\n

25r2<\/sup>+20r+4<\/p>\n\n\n\n

Now\u00a0use the formula for factorizing perfect square\u00a0trinomials.<\/p>\n\n\n\n

a2<\/sup>+2ab+b2<\/sup> = (a+b)2<\/sup><\/p>\n\n\n\n

(5r)2<\/sup>+25r2+22<\/sup> = (5r+2)2<\/sup><\/p>\n\n\n\n

25r2<\/sup>+20r+4 = (5r+2)2<\/sup><\/p>\n\n\n\n

The factorised form of 25r2<\/sup>+20r+4 is (5r+2)2<\/sup>.<\/p>\n\n\n\n

Finally, check your work.<\/p>\n\n\n\n

(5r+2)2<\/sup><\/p>\n\n\n\n

(5r+2)(5r+2) Expand<\/p>\n\n\n\n

25r2<\/sup>+10r+10r+4 Apply the distributive property (FOIL)<\/p>\n\n\n\n

25r2<\/sup>+20r+4<\/p>\n\n\n\n

Yes, 25r2<\/sup>+20r+4=(5r+2)2<\/sup>.<\/p>\n<\/div><\/div>\n\n\n\n

\n
\n

\u27a1\ufe0f Factorise.<\/p>\n\n\n\n

9x2<\/sup>\u20131<\/p>\n<\/div><\/div>\n\n\n\n

Notice that 9x2<\/sup>\u20131 is a difference of squares, because it can be written in the form a2<\/sup>\u2013b2<\/sup>, where a is 3x and b is 1.<\/p>\n\n\n\n

a2<\/sup>\u2013b2<\/sup><\/p>\n\n\n\n

(3x)2<\/sup>\u201312<\/sup><\/p>\n\n\n\n

9x2<\/sup>\u20131<\/p>\n\n\n\n

Now use the formula for factorising a difference of squares.<\/p>\n\n\n\n

a2<\/sup>\u2013b2<\/sup> = (a+b)(a\u2013b)<\/p>\n\n\n\n

(3x)2<\/sup>\u201312 <\/sup>= (3x+1)(3x\u20131)<\/p>\n\n\n\n

9x2<\/sup>\u20131 = (3x+1)(3x\u20131)<\/p>\n\n\n\n

The factorised form of 9x2<\/sup>\u20131 is (3x+1)(3x\u20131).<\/p>\n\n\n\n

Finally, check your work.<\/p>\n\n\n\n

(3x+1)(3x\u20131)<\/p>\n\n\n\n

9x2<\/sup>+3x\u20133x\u20131 Apply the distributive property (FOIL)<\/p>\n\n\n\n

9x2<\/sup>\u20131 <\/p>\n\n\n\n

Yes, 9x2<\/sup>\u20131=(3x+1)(3x\u20131).<\/p>\n<\/div><\/div>\n\n\n\n

\n
\n

\u27a1\ufe0f Factorise.<\/p>\n\n\n\n

9g2<\/sup>\u201325<\/p>\n<\/div><\/div>\n\n\n\n

Notice that 9g2<\/sup>\u201325 is a difference of squares, because it can be written in the form a2<\/sup>\u2013b2<\/sup>, where a is 3g and b is 5.<\/p>\n\n\n\n

a2<\/sup>\u2013b2<\/sup><\/p>\n\n\n\n

(3g)2<\/sup>\u201352<\/sup><\/p>\n\n\n\n

9g2<\/sup>\u201325<\/p>\n\n\n\n

Now use the formula for factorising a difference of squares.<\/p>\n\n\n\n

a2<\/sup>\u2013b2<\/sup> = (a+b)(a\u2013b)<\/p>\n\n\n\n

(3g)2<\/sup>\u201352<\/sup> = (3g+5)(3g\u20135)<\/p>\n\n\n\n

9g2<\/em><\/sup>\u201325 = (3g+5)(3g\u20135)<\/p>\n\n\n\n

The factorised form of 9g2<\/sup>\u201325 is (3g+5)(3g\u20135).<\/p>\n\n\n\n

Finally, check your work.<\/p>\n\n\n\n

(3g+5)(3g\u20135)<\/p>\n\n\n\n

9g2<\/sup>+15g\u201315g\u201325 Apply the distributive property (FOIL)<\/p>\n\n\n\n

9g2<\/sup>\u201325<\/p>\n\n\n\n

Yes, 9g2<\/sup>\u201325=(3g+5)(3g\u20135).<\/p>\n<\/div><\/div>\n\n\n\n

let’s practice!<\/p>\n\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n\n
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\"\"<\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Factorise quadratics: special cases key notes: Factorizing\u00a0perfect square\u00a0trinomials: a2+2ab+b2=(a+b)2 a2\u20132ab+b2=(a\u2013b)2 Factorizing a difference of squares: a2\u2013b2=(a+b)(a\u2013b) Learn with an example \u27a1\ufe0f Factorise. 25r2+20r+4 Notice that 25r2+20r+4 is a perfect square trinomial because it can be written in the form a2+2ab+b2, where a is 5r and b is 2. a2+2ab+b2 (5r)2+25r2+22 25r2+20r+4 Now\u00a0use the formula forContinue reading “AA.5 Factorise quadratics: special cases”<\/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-454","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/454","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=454"}],"version-history":[{"count":8,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/454\/revisions"}],"predecessor-version":[{"id":12195,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/454\/revisions\/12195"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=454"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}