{"id":176,"date":"2022-04-13T10:14:32","date_gmt":"2022-04-13T10:14:32","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=176"},"modified":"2025-01-22T09:49:52","modified_gmt":"2025-01-22T09:49:52","slug":"i-5-factorise-quadratics-special-cases","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/i-5-factorise-quadratics-special-cases\/","title":{"rendered":"I.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

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

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

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

\n
\n

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

25z2<\/sup>\u201316=___________<\/p>\n<\/div><\/div>\n\n\n\n

Notice that 25z2<\/sup>\u201316 is a difference of squares, because it can be written in the form a2<\/sup>\u2013b2<\/sup>, where a is 5<\/strong>z and b is 4<\/strong>.<\/p>\n\n\n\n

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

(5<\/strong>z)2<\/sup>\u20134<\/strong>2<\/sup><\/p>\n\n\n\n

25z2<\/sup>\u201316<\/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

(5<\/strong>z)2<\/sup>\u20134<\/strong>2<\/sup>=(5<\/strong>z+4<\/strong>)(5<\/strong>z\u20134<\/strong>)<\/p>\n\n\n\n

25z2<\/sup>\u201316=(5z+4)(5z\u20134)<\/p>\n\n\n\n

The factorised form of 25z2<\/sup>\u201316 is (5z+4)(5z\u20134).<\/p>\n\n\n\n

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

(5z+4)(5z\u20134)<\/p>\n\n\n\n

25z2<\/sup>+20z\u201320z\u201316Apply the distributive property (FOIL)<\/p>\n\n\n\n

25z2<\/sup>\u201316<\/p>\n\n\n\n

Yes, 25z2<\/sup>\u201316=(5z+4)(5z\u20134). <\/p>\n<\/div><\/div>\n\n\n\n

\n
\n

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

f2<\/sup>\u20138f+16=_________________<\/p>\n<\/div><\/div>\n\n\n\n

Notice that f2<\/sup>\u20138f+16 is a perfect square trinomial because it can be written in the form a2<\/sup>\u20132ab+b2<\/sup>, where a is f and b is 4<\/strong>.<\/p>\n\n\n\n

a2<\/sup>\u20132ab+b2<\/sup><\/p>\n\n\n\n

f2<\/sup>\u20132f . 4<\/strong>+4<\/strong>2<\/sup><\/p>\n\n\n\n

f2<\/sup>\u20138f+16<\/p>\n\n\n\n

Now use the formula for factorising perfect square trinomials.<\/p>\n\n\n\n

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

f2<\/sup>\u20132f . 4<\/strong>+4<\/strong>2<\/sup>=(f\u20134<\/strong>)2<\/sup><\/p>\n\n\n\n

f2<\/sup>\u20138f+16=(f\u20134)2<\/sup><\/p>\n\n\n\n

The factorised form of f2<\/sup>\u20138f+16 is (f\u20134)2<\/sup>.<\/p>\n\n\n\n

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

(f\u20134)2<\/sup><\/p>\n\n\n\n

(f\u20134)(f\u20134)Expand<\/p>\n\n\n\n

f2<\/sup>\u20134f\u20134f+16 Apply the distributive property (FOIL)<\/p>\n\n\n\n

f2<\/sup>\u20138f+16<\/p>\n\n\n\n

Yes, f2<\/sup>\u20138f+16=(f\u20134)2<\/sup>.<\/p>\n<\/div><\/div>\n\n\n\n

\n
\n

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

q2<\/sup>\u20134q+4=____________________<\/p>\n<\/div><\/div>\n\n\n\n

Notice that q2<\/sup>\u20134q+4 is a perfect square trinomial because it can be written in the form a2<\/sup>\u20132ab+b2<\/sup>, where a is q and b is 2<\/strong>.<\/p>\n\n\n\n

a2<\/sup>\u20132ab+b2<\/sup><\/p>\n\n\n\n

q2<\/sup>\u20132q . 2<\/strong>+2<\/strong>2<\/sup><\/p>\n\n\n\n

q2<\/sup>\u20134q+4<\/p>\n\n\n\n

Now use the formula for factorising perfect square trinomials.<\/p>\n\n\n\n

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

q2<\/sup>\u20132q . 2<\/strong>+2<\/strong>2<\/sup>=(q\u20132<\/strong>)2<\/sup><\/p>\n\n\n\n

q2<\/sup>\u20134q+4=(q\u20132)2<\/sup><\/p>\n\n\n\n

The factorised form of q2<\/sup>\u20134q+4 is (q\u20132)2<\/sup>.<\/p>\n\n\n\n

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

(q\u20132)2<\/sup><\/p>\n\n\n\n

(q\u20132)(q\u20132)Expand<\/p>\n\n\n\n

q2<\/sup>\u20132q\u20132q+4Apply the distributive property (FOIL)<\/p>\n\n\n\n

q2<\/sup>\u20134q+4<\/p>\n\n\n\n

Yes, q2<\/sup>\u20134q+4=(q\u20132)2<\/sup>.<\/p>\n<\/div><\/div>\n\n\n\n

let’s practice!<\/p>\n\n\n\n

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

Factorise quadratics: special cases key notes: Factorizing a difference of squares: a2\u2013b2=(a+b)(a\u2013b) a2+2ab+b2=(a+b)2 a2\u20132ab+b2=(a\u2013b)2 Learn with an example Factorise. 25z2\u201316=___________ Notice that 25z2\u201316 is a difference of squares, because it can be written in the form a2\u2013b2, where a is 5z and b is 4. a2\u2013b2 (5z)2\u201342 25z2\u201316 Now use the formula for factorising a difference of squares. a2\u2013b2=(a+b)(a\u2013b) (5z)2\u201342=(5z+4)(5z\u20134) 25z2\u201316=(5z+4)(5z\u20134) The factorised form of 25z2\u201316 is (5z+4)(5z\u20134). Finally, check your work. (5z+4)(5z\u20134) 25z2+20z\u201320z\u201316Apply the distributive property (FOIL) 25z2\u201316Continue reading “I.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-176","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/176","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=176"}],"version-history":[{"count":18,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/176\/revisions"}],"predecessor-version":[{"id":17433,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/176\/revisions\/17433"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=176"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}