{"id":28085,"date":"2021-07-03T11:24:40","date_gmt":"2021-07-03T05:54:40","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=28085"},"modified":"2022-03-02T10:30:27","modified_gmt":"2022-03-02T05:00:27","slug":"ncert-solutions-for-class-8-maths-chapter-14-ex-14-2","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-8-maths-chapter-14-ex-14-2\/","title":{"rendered":"NCERT Solutions for Class 8 Maths Chapter 14 Factorization Ex 14.2"},"content":{"rendered":"

These NCERT Solutions for Class 8 Maths<\/a> Chapter 14 Factorization Ex 14.2 Questions and Answers are prepared by our highly skilled subject experts.<\/p>\n

NCERT Solutions for Class 8 Maths Chapter 14 Factorization Exercise 14.2<\/h2>\n

Question 1.
\nFactorise the following expressions.
\n(i) a2<\/sup> + 8a + 16
\n(ii) p2<\/sup> – lOp + 25
\n(iii) 25m2<\/sup> + 30m+ 9
\n(iv) 49y2<\/sup> + 84yz + 36z2<\/sup>
\n(v) 4x2<\/sup> – 8x + 4
\n(vi) 121b2<\/sup> – 88bc + 16c2<\/sup>
\n(vii) (1 + m)2<\/sup> – 4lm
\n(viii) a4<\/sup> + 2a2<\/sup>b2<\/sup> + b4
\n(Hint: Expand (1 + m)2<\/sup> first)
\nAnswer:
\n(i) a2<\/sup> + 8a + 16
\n= a2<\/sup> + 2 x a x 4 + 42<\/sup>
\n= (a + 4)2<\/sup>
\n= (a + 4) (a + 4)
\n(ii) p2<\/sup> – 10p + 25
\n= p2<\/sup> – 2 x 5p + 52<\/sup>– (p – 5)2<\/sup>
\n= (p – 5) (p – 5)<\/p>\n

\"NCERT<\/p>\n

(iii) 25m2<\/sup> + 30m + 9
\n= (5m)2<\/sup> + 2 x 5m x 3 + 32<\/sup>
\n= (5m + 3)2<\/sup>
\n= (5m + 3) (5m +3)<\/p>\n

(iv) 49y2<\/sup> + 84yz + 36z2<\/sup>
\n= (7y)2<\/sup>+ 2 x 7y x 6z + (6z)2<\/sup>
\n= (7y + 6z)2<\/sup> = (7y + 6z) (7y + 6z)<\/p>\n

(v) 4x2<\/sup> – 8x + 4
\n= (2x)2<\/sup> – 2 x 2x x 2 + 22<\/sup>
\n= (2x – 2)2<\/sup> = 22<\/sup> (x – 1)2<\/sup>
\n= 4 (x – 1) (x – 1)<\/p>\n

(vi) 12lb2<\/sup> – 88bc + 16c2<\/sup>
\n= (11b)2<\/sup> – 2 x 11b x 4c + (4c)2<\/sup>
\n= (11b – 4c)2<\/sup>
\n= (11b – 4c) (11b – 4c)<\/p>\n

(vii) (l + m)2<\/sup> – 4lm
\n= l2<\/sup> + 2lm + m2<\/sup> – 4lm
\n= l2<\/sup> + (21m – 41m) + m2<\/sup>
\n= 1 – 21m + m2<\/sup>
\n= (1 – m)2<\/sup> = (1 – m) (1 – m)<\/p>\n

(viii) a4<\/sup> + 2a2<\/sup> b2<\/sup> + b4<\/sup>
\n= (a2<\/sup>)2<\/sup> + 2 x a2<\/sup> x b2<\/sup> + (b2<\/sup>)2<\/sup>
\n= (a2<\/sup> + b2<\/sup>)2<\/sup>
\n= (a2<\/sup> + b2<\/sup>) (a2<\/sup> + b2<\/sup>)<\/p>\n

\"NCERT<\/p>\n

Question 2.
\nFactorise
\n(i) 4p2<\/sup> – 9q2<\/sup>
\n(ii) 63a2<\/sup> – 112b2<\/sup>
\n(iii) 49x2<\/sup> – 36
\n(iv) 16x5<\/sup> – 144x3<\/sup>
\n(v) (l + m)2<\/sup> – (l – m)2<\/sup>
\n(vi) 9x2<\/sup>y2<\/sup> – 16
\n(vii) (x2<\/sup> – 2xy + y2<\/sup>) – z2<\/sup>
\n(viii) 25a2<\/sup> – 4b2<\/sup> + 28bc – 49c2<\/sup>
\nAnswer:
\n(i) 4p2<\/sup> – 9q2<\/sup>
\n= (2p)2<\/sup> – (3q)2<\/sup>
\n= (2p + 3q) (2p – 3q)
\n[a2<\/sup> – b2<\/sup> = (a + b) (a – b)]<\/p>\n

(ii) 63a2<\/sup>-112<\/sup>b2<\/sup>
\n= 7 x (9a2<\/sup> – 16b2<\/sup>)
\n= 7[(3a)2<\/sup> – (4b)2<\/sup> ]
\n= 7 (3a + 4b) (3a – 4b)
\n[a2<\/sup> – b2<\/sup> = (a + b) (a – b)]<\/p>\n

(iii) 49x2<\/sup> – 36
\n= (7x)2<\/sup> – 62<\/sup> = (7x + 6) (7x – 6)
\n[Using a2<\/sup> – b2<\/sup> = (a + b) (a – b)]<\/p>\n

(iv) 16x3<\/sup> – 144x3<\/sup>
\n= x3<\/sup> [16×2 – 144]
\n= x3<\/sup> x 16 [x2<\/sup> – 9]
\n= 16x3<\/sup> [x2<\/sup> – 32<\/sup>]
\n= 16x3<\/sup> (x + 3) (x – 3)<\/p>\n

\"NCERT<\/p>\n

(v) (l + m)2<\/sup> – (l – m)2<\/sup>
\n= (l + m + l – m) [l + m – (l – m)]
\n= 2l [l + m – l + m]
\n= 2l x 2m = 4lm<\/p>\n

(vi) 9x2<\/sup>y2<\/sup> – 16
\n= (3xy)2<\/sup> – 42<\/sup>
\n= (3xy + 4) (3xy – 4)<\/p>\n

(vii) (x2<\/sup> – 2xy + y2<\/sup>) – z2<\/sup>
\n= [x2<\/sup> – 2xy + y2<\/sup>] – z2<\/sup>
\n= (x – y)2<\/sup> – z2<\/sup>
\n= (x – y + z) (x – y – z)<\/p>\n

(viii) 25a2<\/sup> – 4b2<\/sup> + 28bc – 49c2<\/sup>
\n= 25a2<\/sup> – [4b2<\/sup> – 28bc + 49c2<\/sup> ]
\n= (5a)2<\/sup> – [(2b)2<\/sup> – 2 x 2b x 7c + (7c)2<\/sup>]
\n= (5a)2<\/sup> – (2b – 7c)2<\/sup>
\n= (5a + 2b – 7c) [5a – (2b – 7c)]
\n= (5a + 2b – 7c)(5a – 2b + 7c)<\/p>\n

Question 3.
\nFactorise the expressions.
\n(i) ax2<\/sup> + bx
\n(ii) 7p2<\/sup> + 21q2<\/sup>
\n(iii) 2x3<\/sup> + 2xy2<\/sup> + 2xz2<\/sup>
\n(iv) am2<\/sup> + bm2<\/sup> + bn2<\/sup> + an2<\/sup>
\n(v) (lm + 1) + m + 1
\n(vi) y (y + z) + 9 (y + z)
\n(vii) 5y2<\/sup> – 20y – 8z + 2yz
\n(viii) 10ab + 4a + 5b + 2
\n(ix) 6xy – 4y + 6 – 9x
\nAnswer:
\n(i) ax2<\/sup> + bx
\n= a x x x x + b x x
\n= x (ax + b)<\/p>\n

\"NCERT<\/p>\n

(ii) 7p2<\/sup> + 21q2<\/sup>
\n= 7 x p x p + 3 x 7 x q x q – 7 (p2<\/sup> + 3q2<\/sup>)<\/p>\n

(iii) 2x3<\/sup> + 2xy2<\/sup> + 2xz2<\/sup>
\n= 2 x x x x x x + 2 x x x y x y + 2 x x x z x z
\n= 2x(x xx + yxy + zxz)
\n= 2x (x2<\/sup> + y2<\/sup> + z2<\/sup>)<\/p>\n

(iv) am2<\/sup> + bm2<\/sup> + bn2<\/sup> + an2<\/sup>
\n= m2<\/sup> (a + b) + n2<\/sup> (b + a)
\n= m2<\/sup> (a + b) + n2<\/sup> (a + b)
\n= (a + b) (m2<\/sup> + n2<\/sup>)<\/p>\n

(v) (lm + l) + m + l
\n= l(m + l) + l(m + l)
\n= (m + l) (l + l)<\/p>\n

(vi) y (y + z) + 9 (y + z)
\n= (y + z) (y + 9)
\n[(y + z) is common for both terms)]<\/p>\n

(vii) 5y2<\/sup> – 20y – 8z + 2yz
\n= 5y x y – 4 x 5y – 2 x 2 x 2 x z + 2 x y x z
\n= 5y (y – 4) + 2z (- 4 + y)
\n= 5y (y – 4) + 2z (y – 4)
\n= (y – 4) (5y + 2z)<\/p>\n

(viii) 10ab + 4a + 5b + 2
\n= 2 x 5 x a x b + 2 x 2 x a + 5 x b + 2
\n= 2a (5b + 2) + 1 (5b + 2)
\n= (5b + 2) (2a + 1)<\/p>\n

\"NCERT<\/p>\n

(ix) 6xy – 4y + 6 – 9x
\n= 2 x 3 x x x y – 2 x 2 x y + 2 x 3 – 3 x 3 x x
\n= 2y (3x – 2) + 3 (2 – 3x)
\n= 2y (3x – 2) – 3 (3x – 2)
\n= (3x – 2) (2y – 3)<\/p>\n

Question 4.
\nFactorise
\n(i) a4<\/sup> – b4<\/sup>
\n(ii) p4<\/sup> – 81
\n(iii) x4<\/sup> – (y + z)4<\/sup>
\n(iv) x24<\/sup> – (x – z)
\n(v) a4<\/sup> – 2a2<\/sup>b2<\/sup> + b4<\/sup>
\nAnswer:
\n(i) a4<\/sup> – b4<\/sup>
\n= (a2<\/sup>)2<\/sup> – (b2<\/sup>)2<\/sup>
\n[(using a2<\/sup> – b2<\/sup> = (a + b) (a – b)]
\n= (a2<\/sup> + b2<\/sup>) (a2<\/sup> – b2<\/sup>)
\n= (a2<\/sup> + b2<\/sup>) (a + b) (a – b)<\/p>\n

(ii) p4<\/sup> – 81
\n= (p2<\/sup>)2<\/sup> – 92<\/sup>
\n[Using a2<\/sup> – b2<\/sup> = (a + b) (a – b)]
\n= (p2<\/sup> + 9) (p2<\/sup> – 9)
\n= (P2<\/sup> + 9) [p2<\/sup> – 32 ]
\n= (p2<\/sup> + 9) (p + 3) (p – 3)<\/p>\n

(iii) x2<\/sup> – (y + z)4
\n= (x2<\/sup>)2<\/sup> – [(y + z)2<\/sup>]2<\/sup>
\n[using a2<\/sup> – b2<\/sup> = (a + b) (a – b)
\n= [x2<\/sup> + (y + z)2<\/sup>] [x2<\/sup> – (y + z)2<\/sup>]
\n= [x2<\/sup> + (y + z2<\/sup>)] (x + y + z) [x – (y + z)
\n= [x2<\/sup> + (y + z)2<\/sup>] [x + y + z) (x – y – z)<\/p>\n

(iv) x4<\/sup> – (x – z)4<\/sup>
\n= (x2<\/sup>)2<\/sup> – [(x-z)2<\/sup>]2<\/sup>
\n= [x2<\/sup> + (x – z)2<\/sup>] [x2<\/sup> – (x – z)2<\/sup>]
\n[Using a2<\/sup> – b2<\/sup> = (a + b) (a – b)]
\n= [x2<\/sup> + (x – z)2<\/sup> ] [(x + x – z) (x – x + z)]
\n= [x2<\/sup> + (x – z)2<\/sup>] (2x – z) (z)
\n= (x2<\/sup> + x2<\/sup> + z2<\/sup> – 2xz) (2x – z) (z)
\n= (2x2<\/sup> + z2<\/sup> – 2xz) (2x – z) (z)
\n= z (2x – z) (2x2<\/sup> + z2<\/sup> – 2xz)<\/p>\n

\"NCERT<\/p>\n

(v) a4<\/sup> – 2a2<\/sup> b2<\/sup> + b4<\/sup>
\n= (a2<\/sup>)2<\/sup> – 2 x a2<\/sup> x b2<\/sup> + (b2<\/sup>)2<\/sup> = (a2<\/sup> – b2<\/sup> )2<\/sup>
\n= (a2<\/sup> – b2<\/sup>) x (a2<\/sup> – b2<\/sup>)
\n= (a + b) (a – b) (a + b) (a – b)
\n= (a + b)2<\/sup> (a – b)2<\/sup><\/p>\n

Question 5.
\nFactorise the following expressions.
\n(i) p2<\/sup> + 6p + 8
\n(ii) q2<\/sup> – lOq + 21
\n(iii) p2<\/sup> + 6p – 16
\nAnswer:
\n(i) p2<\/sup> + 6p + 8
\n= p2<\/sup> + 4p + 2p + 8
\n[8 = 2 x 4 and 2 + 4 = 6]
\n= p (p + 4) + 2 (p + 4)
\n= (p + 4) (p + 2)<\/p>\n

(ii) q2<\/sup> – 10q + 21
\n= q2<\/sup> – 7q – 3q + 21
\n[21 = – 7 x – 3 and – 10 = – 7 – 3]
\n= q(q – 7) – 3(q – 7)
\n= (q – 7) (q – 3)<\/p>\n

(iii) p2<\/sup> + 6p – 16
\n= p2<\/sup> + 8p – 2p – 16
\n[-16 = 8 x – 2 and 8 – 2 = 6]
\n= p(p + 8) – 2 (p + 8)
\n= (p + 8) (p – 2)2<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 8 Maths Chapter 14 Factorization Ex 14.2 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 8 Maths Chapter 14 Factorization Exercise 14.2 Question 1. Factorise the following expressions. (i) a2 + 8a + 16 (ii) p2 – lOp + 25 (iii) 25m2 + …<\/p>\n

NCERT Solutions for Class 8 Maths Chapter 14 Factorization Ex 14.2<\/span> Read More »<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"default","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","spay_email":""},"categories":[7],"tags":[],"yoast_head":"\nNCERT Solutions for Class 8 Maths Chapter 14 Factorization Ex 14.2 - MCQ Questions<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-8-maths-chapter-14-ex-14-2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for Class 8 Maths Chapter 14 Factorization Ex 14.2 - MCQ Questions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 8 Maths Chapter 14 Factorization Ex 14.2 Questions and Answers are prepared by our highly skilled subject experts. 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NCERT Solutions for Class 8 Maths Chapter 14 Factorization Exercise 14.2 Question 1. Factorise the following expressions. (i) a2 + 8a + 16 (ii) p2 – lOp + 25 (iii) 25m2 + … NCERT Solutions for Class 8 Maths Chapter 14 Factorization Ex 14.2 Read More »","og_url":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-8-maths-chapter-14-ex-14-2\/","og_site_name":"MCQ Questions","article_publisher":"https:\/\/www.facebook.com\/NCERTSolutionsGuru\/","article_published_time":"2021-07-03T05:54:40+00:00","article_modified_time":"2022-03-02T05:00:27+00:00","og_image":[{"url":"https:\/\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png"}],"twitter_card":"summary_large_image","twitter_creator":"@ncertsolguru","twitter_site":"@ncertsolguru","twitter_misc":{"Written by":"Prasanna","Est. reading time":"8 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebSite","@id":"https:\/\/mcq-questions.com\/#website","url":"https:\/\/mcq-questions.com\/","name":"MCQ Questions","description":"MCQ Questions for Class 1 to 12","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mcq-questions.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-8-maths-chapter-14-ex-14-2\/#primaryimage","inLanguage":"en-US","url":"https:\/\/i0.wp.com\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png?fit=170%2C17&ssl=1","contentUrl":"https:\/\/i0.wp.com\/mcq-questions.com\/wp-content\/uploads\/2021\/01\/NCERT-Solutions-Guru.png?fit=170%2C17&ssl=1","width":170,"height":17,"caption":"NCERT Solutions"},{"@type":"WebPage","@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-8-maths-chapter-14-ex-14-2\/#webpage","url":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-8-maths-chapter-14-ex-14-2\/","name":"NCERT Solutions for Class 8 Maths Chapter 14 Factorization Ex 14.2 - MCQ Questions","isPartOf":{"@id":"https:\/\/mcq-questions.com\/#website"},"primaryImageOfPage":{"@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-8-maths-chapter-14-ex-14-2\/#primaryimage"},"datePublished":"2021-07-03T05:54:40+00:00","dateModified":"2022-03-02T05:00:27+00:00","author":{"@id":"https:\/\/mcq-questions.com\/#\/schema\/person\/4ba9570f32f2057e70e670c7885e47f3"},"breadcrumb":{"@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-8-maths-chapter-14-ex-14-2\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mcq-questions.com\/ncert-solutions-for-class-8-maths-chapter-14-ex-14-2\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-8-maths-chapter-14-ex-14-2\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mcq-questions.com\/"},{"@type":"ListItem","position":2,"name":"NCERT Solutions for Class 8 Maths Chapter 14 Factorization Ex 14.2"}]},{"@type":"Person","@id":"https:\/\/mcq-questions.com\/#\/schema\/person\/4ba9570f32f2057e70e670c7885e47f3","name":"Prasanna","image":{"@type":"ImageObject","@id":"https:\/\/mcq-questions.com\/#personlogo","inLanguage":"en-US","url":"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g","caption":"Prasanna"},"url":"https:\/\/mcq-questions.com\/author\/prasanna\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/posts\/28085"}],"collection":[{"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/users\/9"}],"replies":[{"embeddable":true,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/comments?post=28085"}],"version-history":[{"count":1,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/posts\/28085\/revisions"}],"predecessor-version":[{"id":33859,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/posts\/28085\/revisions\/33859"}],"wp:attachment":[{"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/media?parent=28085"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/categories?post=28085"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/tags?post=28085"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}