{"id":28086,"date":"2021-07-03T11:23:06","date_gmt":"2021-07-03T05:53:06","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=28086"},"modified":"2022-03-02T10:30:27","modified_gmt":"2022-03-02T05:00:27","slug":"ncert-solutions-for-class-8-maths-chapter-14-ex-14-1","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-8-maths-chapter-14-ex-14-1\/","title":{"rendered":"NCERT Solutions for Class 8 Maths Chapter 14 Factorization Ex 14.1"},"content":{"rendered":"

These NCERT Solutions for Class 8 Maths<\/a> Chapter 14 Factorization Ex 14.1 Questions and Answers are prepared by our highly skilled subject experts.<\/p>\n

NCERT Solutions for Class 8 Maths Chapter 14 Factorization Exercise 14.1<\/h2>\n

Question 1.
\nFind the common factors of the given terms.
\n(i) 12x, 36
\n(ii) 2y, 22xy
\n(iii) 14pq, 28p2<\/sup>q2<\/sup>
\n(iv) 2x, 3x2<\/sup>, 4
\n(v) 6 abc, 24ab2<\/sup>, 12 a2<\/sup>b
\n(vi) 16x3<\/sup>, – 4x2<\/sup>, 32x
\n(vii) 10 pq, 20 qr, 30rp
\n(viii) 3x2<\/sup>y3<\/sup>, 10x3<\/sup>, 6x2<\/sup>y2<\/sup>z
\nAnswer:
\n(i) 12x = 2 x 2 x 3 x x
\n36 = 2 x 2 x 3 x 3
\n\u2234 The common factor = 2 x 2 x 3 = 12<\/p>\n

(ii) 2y = 2 x y
\n22y = 2 x 11 x y
\n\u2234 The common factor = 2 x y = 2y<\/p>\n

(iii) 14pq = 2 x 7 x p x q
\n28 p2<\/sup>q2<\/sup> = 2 x 2 x 7 x p x p x q x q
\n\u2234 The common factor
\n= 2 x 7 x p x q = 14pq<\/p>\n

\"NCERT<\/p>\n

(iv) 2x = 2 x x
\n3x2<\/sup> = 3 x x x x
\n4 = 2 x 2
\n\u2234 Common factor = 1
\n(1 is a factor of every term)<\/p>\n

(v) 6abc = 2 x 3 x a x b x c
\n24ab2<\/sup> = 2 x 2 x 2 x 3 x a x b x b
\n12a2<\/sup>b = 2 x 2 x 3 x a x a x b
\n\u2234 The common factor
\n= 2 x 3 x a x b = 6ab<\/p>\n

(vi) 16x3<\/sup> = 2 x 2 x 2x 2 x x x x x x
\n-4x2<\/sup> = -1 x 2 x 2 x x x x
\n32x = 2 x 2 x 2 x 2 x 2 x x
\n\u2234 The common factor = 2 x 2 x x = 4x<\/p>\n

(vii) 10pq = 2 x 5 x p x q
\n20qr = 2 x 2 x 5x q x r
\n30rp = 2 x 3 x 5 x r x p
\n\u2234\u00a0 The common factor = 2 x 5 = 10<\/p>\n

(viii) 3x2<\/sup>y3<\/sup> = 3 x x x x x y x y x y
\n10x3<\/sup>y2<\/sup> = 2 x 5 x x x x x x x y x y
\n6x2<\/sup>y2<\/sup>z = 2 x 3 x x x x x y x y x z
\n\u2234\u00a0 The common factor = x x x x y x y
\n= x2<\/sup>y2<\/sup><\/p>\n

Question 2.
\nFactorise the following expressions.
\n(i) 7x – 42
\n(ii) 6p – 12q
\n(iii) 7a2<\/sup> + 14a
\n(iv) – 16 z + 20 z3<\/sup>
\n(v) 20 l2<\/sup> m + 30 alm
\n(vi) 5x2<\/sup>y – 15xy2<\/sup>
\n(vii) 10a2<\/sup> + 15 b2<\/sup> + 20c2<\/sup>
\n(viii) – 4a2<\/sup> + 4ab – 4ca
\n(ix) x2<\/sup>yz + xyz2<\/sup> xy2<\/sup>z xyz2<\/sup>
\n(x) ax2<\/sup>y + bxy2<\/sup> + cxyz
\nAnswer:
\n(i) 7x – 42
\n=7 x x – 2 x 3 x 7
\n= 7 (x – 2 x 3)
\n= 7 (x – 6)<\/p>\n

(ii) 6p – 12q
\n= 2 x 3p – 2 x 2 x 3 x q
\n= 2 x 3 [p – 2 x q]
\n= 6 (p – 2q)<\/p>\n

\"NCERT<\/p>\n

(iii) 7a2<\/sup> + 14a
\n=7 x a x a + 2 x 7 x a
\n= 7a (a + 2)<\/p>\n

(iv) – 16z + 20 z3<\/sup>
\n= -2 x 2 x 2 x 2 x z + 2 x 2 x 5 x z x z x z
\n= 2 x 2 x z [-2x2<\/sup> + 5 x z x z]
\n= 4z (-4 + 5z2<\/sup>)<\/p>\n

(v) 20 l2<\/sup>m + 30 alm
\n= 2 x 2 x 5 x l x l x m + 2 x 3 x 5 x a x l x m
\n= 2 x 5 x l x m[2 x l + 3a]
\n= 10lm (2l + 3a)<\/p>\n

(vi) 5x2<\/sup>y-15xy2<\/sup>
\n=5 x x x x x y – 3 x 5 x x x y x x
\n= 5xy (x – 3y)<\/p>\n

(vii) 10a2<\/sup> – 15b2<\/sup> + 20c2<\/sup>
\n= 2 x 5 x a x a – 3 x 5 x b x b + 2 x 2 x 5 x c x c
\n= 5[2 x a x a – 3 x b x b + 2 x 2 x c x c]
\n= 5 (2a2<\/sup> – 3b2<\/sup> + 4c2<\/sup>)<\/p>\n

(viii) -4a2<\/sup> + 4ab – 4ca
\n= -2 x 2 x a x a + 2 x 2 x a x b – 2 x 2 x c x a
\n= 2 x 2 x a (-a + b – c)
\n= 4a (-a + b – c)<\/p>\n

(ix) x2<\/sup>yz + xy2<\/sup>z + xyz2<\/sup>
\n= x x x x y x z + x x y x y x z + x x y x z x z
\n= x x y x z[x + y + z]
\n= xyz (x + y + z)<\/p>\n

(x) ax2<\/sup>y + bxy2<\/sup> + cxyz
\n= a x x x x x y + b x x x y x y + c x x x y x z
\n= x x y[a x x + b x y + c x z]
\n= xy (ax + by + cz)<\/p>\n

\"NCERT<\/p>\n

Question 3.
\nFactorise
\n(i) x2<\/sup> + xy + 8x + 8y
\n(ii) 15xy – 6x + 5y – 2
\n(iii) ax + bx – ay – by
\n(iv) 15pq + 15 + 9q – 25p
\n(v) z – 7 + 7xy – xyz
\nAnswer:
\n(i) x2<\/sup> + xy + 8x + 8y
\n= x(x + y) + 8 (x + y)
\n= (x + y) (x + 8)<\/p>\n

(ii) 15xy – 6x + 5y – 2
\n= 3x (5y – 2) + 1 (5y – 2)
\n= (5y – 2) (3x + 1)<\/p>\n

(iii) ax + bx – ay – by
\n= x (a + b) – y (a + b)
\n= (a + b) (x – y)<\/p>\n

(iv) 15pq + 15 + 9q + 25p
\n= 15pq + 25p + 9q + 15
\n= 5p (3q + 5) + 3 (3q + 5)
\n(Re-arranging the terms)
\n= (3q + 5) (5p + 3)<\/p>\n

\"NCERT<\/p>\n

(v) z – 7 + 7xy – xyz
\n= z – xyz + 7xy – 7
\n= z( 1 – xy) + (7 (xy – 1)
\n(Re-arranging the terms)
\n= z (1 – xy) – 7 (1 – xy)
\n= (1 – xy) (z- 7)<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 8 Maths Chapter 14 Factorization Ex 14.1 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 8 Maths Chapter 14 Factorization Exercise 14.1 Question 1. Find the common factors of the given terms. (i) 12x, 36 (ii) 2y, 22xy (iii) 14pq, 28p2q2 (iv) 2x, …<\/p>\n

NCERT Solutions for Class 8 Maths Chapter 14 Factorization Ex 14.1<\/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 14.1 - 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-14-1\/\" \/>\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 14.1 - MCQ Questions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 8 Maths Chapter 14 Factorization Ex 14.1 Questions and Answers are prepared by our highly skilled subject experts. 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