{"id":3410,"date":"2022-12-14T14:43:30","date_gmt":"2022-12-14T14:43:30","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=3410"},"modified":"2023-01-31T06:50:38","modified_gmt":"2023-01-31T06:50:38","slug":"ncert-solutions-class-8-maths-chapter-14-factorisation-ex-14-1","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-14-factorisation-ex-14-1\/","title":{"rendered":"NCERT Solutions Class 8 Maths Chapter 14 Factorisation Ex 14.1"},"content":{"rendered":"<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">NCERT Solutions Class 8 Mathematics\u00a0<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Chapter &#8211; 14 (Factorisation)\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The NCERT Solutions in English Language for Class 8 Mathematics <strong>Chapter &#8211; 14 Factorisation\u00a0 <\/strong>Exercise 14.1 has been provided here to help the students in solving the questions from this exercise.\u00a0<\/span><\/p>\n<h4><span style=\"color: #000000;\"><strong>Chapter 14: Factorisation<\/strong><\/span><\/h4>\n<ul>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-14-factorisation-ex-14-2\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 8 Maths Ex &#8211; 14.2<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-14-factorisation-ex-14-3\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 8 Maths Ex &#8211; 14.3<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-14-factorisation-ex-14-4\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 8 Maths Ex &#8211; 14.4<\/a><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Exercise &#8211; 14.1<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>1. Find the common factors of the given terms.<br \/>\n<\/strong><strong>(i)<\/strong> 12x, 36<br \/>\n<strong>(ii)<\/strong> 2y, 22xy<br \/>\n<strong>(iii)<\/strong> 14 pq, 28p<sup>2<\/sup>q<sup>2<br \/>\n<\/sup><strong>(iv)<\/strong> 2x, 3x<sup>2<\/sup>, 4<br \/>\n<strong>(v)<\/strong> 6 abc, 24ab<sup>2<\/sup>, 12a<sup>2<\/sup>b<br \/>\n<strong>(vi)<\/strong> 16 x<sup>3<\/sup>, \u2013 4x<sup>2<\/sup>\u00a0, 32 x<br \/>\n<strong>(vii)<\/strong> 10 pq, 20qr, 30 rp<br \/>\n<strong>(viii)<\/strong> 3x<sup>2<\/sup>y<sup>3<\/sup>\u00a0, 10x<sup>3<\/sup>y<sup>2<\/sup>\u00a0, 6x<sup>2<\/sup>y<sup>2<\/sup>z<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i) 12x, 36<br \/>\n<\/strong>Factors of 12x and 36<br \/>\n12x = 2\u00d72\u00d73\u00d7x<br \/>\n36 = 2\u00d72\u00d73\u00d73<br \/>\nCommon factors of 12x and 36 are 2, 2, 3<br \/>\n\u2234 Required common factors = 2\u00d72\u00d73 = 12<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) 2y, 22xy<\/strong><br \/>\nFactors of 2y and 22xy<br \/>\n2y = 2 \u00d7 y<br \/>\n22xy = 2 \u00d7 11 \u00d7 x \u00d7 y<br \/>\nCommon factors of 2y and 22xy are 2, y<br \/>\n\u2234 Required common factors =\u00a0 2 \u00d7 y = 2y<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii) 14 pq, 28p<sup>2<\/sup>q<sup>2<\/sup><\/strong><br \/>\nFactors of 14pq and 28p<sup>2<\/sup>q<sup>2<br \/>\n<\/sup>14pq = 2 x 7 x p x q<br \/>\n28p<sup>2<\/sup>q<sup>2<\/sup> = 2 x 2 x 7 x p x p x q x q<br \/>\nCommon factors of 14 pq and 28 p<sup>2<\/sup>q<sup>2<\/sup> are 2, 7 , p , q<br \/>\n\u2234 Required common factors = 2 x 7 x p x q = 14pq<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iv) 2x, 3x<sup>2<\/sup>, 4<\/strong><br \/>\nFactors of 2x, 3x<sup>2<\/sup>and 4<br \/>\n2x = 2\u00d7x<br \/>\n3x<sup>2<\/sup>= 3\u00d7x\u00d7x<br \/>\n4 = 2\u00d72<br \/>\nCommon factors of 2x, 3x<sup>2\u00a0<\/sup>and 4 is 1.<br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(v) 6 abc, 24ab<sup>2<\/sup>, 12a<sup>2<\/sup>b<\/strong><br \/>\nFactors of 6abc, 24ab<sup>2<\/sup>\u00a0and 12a<sup>2<\/sup>b<br \/>\n6abc = 2\u00d73\u00d7a\u00d7b\u00d7c<br \/>\n24ab<sup>2<\/sup>\u00a0= 2\u00d72\u00d72\u00d73\u00d7a\u00d7b\u00d7b<br \/>\n12 a<sup>2\u00a0<\/sup>b = 2\u00d72\u00d73\u00d7a\u00d7a\u00d7b<br \/>\nCommon factors of 6 abc, 24ab<sup>2<\/sup>\u00a0and 12a<sup>2<\/sup>b are 2, 3, a, b<br \/>\n\u2234 Required common factors = 2\u00d73\u00d7a\u00d7b = 6ab<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(vi) 16 x<sup>3<\/sup>, \u2013 4x<sup>2<\/sup>\u00a0, 32 x<\/strong><br \/>\nFactors of 16x<sup>3\u00a0<\/sup>, -4x<sup>2<\/sup>and 32x<br \/>\n16 x<sup>3\u00a0<\/sup>= 2\u00d72\u00d72\u00d72\u00d7x\u00d7x\u00d7x<br \/>\n\u2013 4x<sup>2<\/sup>\u00a0= -1\u00d72\u00d72\u00d7x\u00d7x<br \/>\n32x = 2\u00d72\u00d72\u00d72\u00d72\u00d7x<br \/>\nCommon factors of 16 x<sup>3\u00a0<\/sup>, \u2013 4x<sup>2\u00a0<\/sup>and 32x are 2,2, x<br \/>\n\u2234 Required common factors = 2\u00d72\u00d7x = 4x<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(vii) 10 pq, 20qr, 30 rp<br \/>\n<\/strong>Factors of 10 pq, 20qr and 30rp<br \/>\n10 pq = 2\u00d75\u00d7p\u00d7q<br \/>\n20qr = 2\u00d72\u00d75\u00d7q\u00d7r<br \/>\n30rp= 2\u00d73\u00d75\u00d7r\u00d7p<br \/>\nCommon factors of 10 pq, 20qr and 30rp are 2, 5<br \/>\n\u2234 Required common factors = 2\u00d75 = 10<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(viii) 3x<sup>2<\/sup>y<sup>3<\/sup>\u00a0, 10x<sup>3<\/sup>y<sup>2<\/sup>\u00a0, 6x<sup>2<\/sup>y<sup>2<\/sup>z<\/strong><br \/>\nFactors of 3x<sup>2<\/sup>y<sup>3<\/sup>\u00a0, 10x<sup>3<\/sup>y<sup>2<\/sup>\u00a0and 6x<sup>2<\/sup>y<sup>2<\/sup>z<br \/>\n3x<sup>2<\/sup>y<sup>3<\/sup>\u00a0= 3\u00d7x\u00d7x\u00d7y\u00d7y\u00d7y<br \/>\n10x<sup>3\u00a0<\/sup>y<sup>2<\/sup>\u00a0= 2\u00d75\u00d7x\u00d7x\u00d7x\u00d7y\u00d7y<br \/>\n6x<sup>2<\/sup>y<sup>2<\/sup>z = 3\u00d72\u00d7x\u00d7x\u00d7y\u00d7y\u00d7z<br \/>\nCommon factors of 3x<sup>2<\/sup>y<sup>3<\/sup>, 10x<sup>3<\/sup>y<sup>2<\/sup>\u00a0and 6x<sup>2<\/sup>y<sup>2<\/sup>z are x<sup>2<\/sup>, y<sup>2<br \/>\n<\/sup>\u2234 Required common factors = x<sup>2<\/sup>\u00d7y<sup>2<\/sup>\u00a0= x<sup>2<\/sup>y<sup>2<\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>2. Factorise the following expressions.<br \/>\n(i)<\/strong> 7x\u201342<br \/>\n<strong>(ii)<\/strong> 6p\u201312q<br \/>\n<strong>(iii)<\/strong> 7a<sup>2<\/sup>+ 14a<br \/>\n<strong>(iv)<\/strong> -16z+20 z<sup>3<br \/>\n<\/sup><strong>(v)<\/strong> 20l<sup>2<\/sup>m+30alm<br \/>\n<strong>(vi)<\/strong> 5x<sup>2<\/sup>y-15xy<sup>2<br \/>\n<\/sup><strong>(vii)<\/strong> 10a<sup>2<\/sup>-15b<sup>2<\/sup>+20c<sup>2<br \/>\n<\/sup><strong>(viii)<\/strong> -4a<sup>2<\/sup>+4ab\u20134 ca<br \/>\n<strong>(ix)<\/strong> x<sup>2<\/sup>yz+xy<sup>2<\/sup>z +xyz<sup>2<br \/>\n<\/sup><strong>(x)<\/strong> ax<sup>2<\/sup>y+bxy<sup>2<\/sup>+cxyz<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n(i)\u00a0<\/strong><strong>7x = 7 \u00d7 x<\/strong><\/span><br \/>\n<span style=\"color: #000000;\">42 = 2 \u00d7 3 \u00d7 7<\/span><br \/>\n<span style=\"color: #000000;\">The common factor is 7.<\/span><br \/>\n<span style=\"color: #000000;\">Therefore, 7x &#8211; 42 = (7 \u00d7 x) &#8211; (2 \u00d7 3 \u00d7 7 )<\/span><br \/>\n<span style=\"color: #000000;\">= 7(x &#8211; 6)<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(ii)\u00a06p -12q<br \/>\n<\/strong>6p = 2 \u00d7 3 \u00d7 p<\/span><br \/>\n<span style=\"color: #000000;\">12q = 2 \u00d7 2 \u00d7 3 \u00d7 q<\/span><br \/>\n<span style=\"color: #000000;\">The common factors are 2 and 3.<\/span><br \/>\n<span style=\"color: #000000;\">Therefore, <\/span><br \/>\n<span style=\"color: #000000;\">6p -12q = (2 \u00d7 3 \u00d7 p) &#8211; (2 \u00d7 2 \u00d7 3 \u00d7 q)<\/span><br \/>\n<span style=\"color: #000000;\">= 2 \u00d7 3(p &#8211; 2 \u00d7 q)<\/span><br \/>\n<span style=\"color: #000000;\">= 6(p &#8211; 2q)<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(iii)\u00a07a<sup>2<\/sup>+14a<br \/>\n<\/strong>7a<sup>2<\/sup>= 7 \u00d7 a \u00d7 a<\/span><br \/>\n<span style=\"color: #000000;\">14a = 2 \u00d7 7 \u00d7 a <\/span><br \/>\n<span style=\"color: #000000;\">The common factors are 7 and a . <\/span><br \/>\n<span style=\"color: #000000;\">Therefore, <\/span><br \/>\n<span style=\"color: #000000;\">7a<sup>2<\/sup>\u00a0+ 14a = (7 \u00d7 a \u00d7 a) + (2 \u00d7 7 \u00d7 a)<\/span><br \/>\n<span style=\"color: #000000;\">= 7 \u00d7 a(a + 2)<\/span><br \/>\n<span style=\"color: #000000;\">= 7a(a + 2)<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(iv)\u00a0-16z + 20z<sup>3<br \/>\n<\/sup><\/strong>16z = -1\u00a0\u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 z<\/span><br \/>\n<span style=\"color: #000000;\">20z<sup>3<\/sup>\u00a0= 2 \u00d7 2 \u00d7 5 \u00d7 z \u00d7 z \u00d7 z<\/span><br \/>\n<span style=\"color: #000000;\">The common factors are 2, 2, and z. <\/span><br \/>\n<span style=\"color: #000000;\">Therefore, <\/span><br \/>\n<span style=\"color: #000000;\">-16z + 20z<sup>3<\/sup>\u00a0<\/span><br \/>\n<span style=\"color: #000000;\">= -(2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 z) + (2 \u00d7 2 \u00d7 5 \u00d7 z \u00d7 z \u00d7 z) <\/span><br \/>\n<span style=\"color: #000000;\">= (2 \u00d7 2 \u00d7 z)[-(2 \u00d7 2) + (5 \u00d7 z \u00d7 z)]<\/span><br \/>\n<span style=\"color: #000000;\">= 4z(-4 + 5z<sup>2<\/sup>)<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(v)\u00a020l<sup>2<\/sup>m + 30alm<br \/>\n<\/strong>20l<sup>2<\/sup>m= 2 \u00d7 2 \u00d7 5 \u00d7 l \u00d7 l \u00d7 m<\/span><br \/>\n<span style=\"color: #000000;\">30alm = 2 \u00d7 3 \u00d7 5 \u00d7 a \u00d7 l \u00d7 m<\/span><br \/>\n<span style=\"color: #000000;\">The common factors are 2, 5, l and m.<\/span><br \/>\n<span style=\"color: #000000;\">Therefore, <\/span><br \/>\n<span style=\"color: #000000;\">20l<sup>2<\/sup>m + 30alm = (2 \u00d7 2 \u00d7 5 \u00d7 l \u00d7 l \u00d7 m) + (2 \u00d7 3 \u00d7 5 \u00d7 a \u00d7 l \u00d7 m)<\/span><br \/>\n<span style=\"color: #000000;\">= (2 \u00d7 5 \u00d7 l \u00d7 m)[(2 \u00d7 l) + (3 \u00d7 a)]<\/span><br \/>\n<span style=\"color: #000000;\">= 10lm(2l + 3a)<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(vi)\u00a05x<sup>2<\/sup>y -15xy<sup>2<br \/>\n<\/sup><\/strong>5x<sup>2<\/sup>y = 5 \u00d7 x \u00d7 x \u00d7 y<\/span><br \/>\n<span style=\"color: #000000;\">15xy<sup>2<\/sup>\u00a0= 3 \u00d7 5 \u00d7 x \u00d7 y \u00d7 y<\/span><br \/>\n<span style=\"color: #000000;\">The common factors are 5, x, and y.<\/span><br \/>\n<span style=\"color: #000000;\">Therefore, <\/span><br \/>\n<span style=\"color: #000000;\">5x<sup>2<\/sup>y &#8211; 15xy<sup>2<\/sup>\u00a0= (5 \u00d7 x \u00d7 x \u00d7 y) &#8211; (3 \u00d7 5 \u00d7 x \u00d7 y \u00d7 y)<\/span><br \/>\n<span style=\"color: #000000;\">= 5 \u00d7 x \u00d7 y[x &#8211; (3 \u00d7 y)]<\/span><br \/>\n<span style=\"color: #000000;\">= 5xy(x &#8211; 3y)<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(vii)\u00a010a<sup>2<\/sup>\u00a0-15b<sup>2<\/sup>\u00a0+ 20c<sup>2<br \/>\n<\/sup><\/strong>10a<sup>2\u00a0<\/sup>= 2 \u00d7 5 \u00d7 a \u00d7 a<\/span><br \/>\n<span style=\"color: #000000;\">15b<sup>2<\/sup>\u00a0= 3 \u00d7 5 \u00d7 b \u00d7 b<\/span><br \/>\n<span style=\"color: #000000;\">20c<sup>2<\/sup>\u00a0= 2 \u00d7 2 \u00d7 5 \u00d7 c \u00d7 c<\/span><br \/>\n<span style=\"color: #000000;\">The common factor is 5. <\/span><br \/>\n<span style=\"color: #000000;\">Therefore, <\/span><br \/>\n<span style=\"color: #000000;\">10a<sup>2<\/sup>\u00a0-15b<sup>2<\/sup>\u00a0+ 20c<sup>2<\/sup>\u00a0= (2 \u00d7 5 \u00d7 a \u00d7 a) &#8211; (3 \u00d7 5 \u00d7 b \u00d7 b) + (2 \u00d7 2 \u00d7 5 \u00d7 c \u00d7 c)<\/span><br \/>\n<span style=\"color: #000000;\">= 5[(2 \u00d7 a \u00d7 a) &#8211; (3 \u00d7 b \u00d7 b) + (2 \u00d7 2 \u00d7 c \u00d7 c)]<\/span><br \/>\n<span style=\"color: #000000;\">= 5(2a<sup>2<\/sup>\u00a0&#8211; 3b<sup>2<\/sup>\u00a0+ 4c<sup>2<\/sup>\u00a0)<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(viii)\u00a0-4a<sup>2<\/sup>\u00a0+ 4ab &#8211; 4ca<br \/>\n<\/strong>4a<sup>2\u00a0<\/sup>= 2 \u00d7 2 \u00d7 a \u00d7 a<\/span><br \/>\n<span style=\"color: #000000;\">4ab = 2 \u00d7 2 \u00d7 a \u00d7 b<\/span><br \/>\n<span style=\"color: #000000;\">4ca = 2 \u00d7 2 \u00d7 c \u00d7 a<\/span><br \/>\n<span style=\"color: #000000;\">The common factors are 2, 2, and a .<\/span><br \/>\n<span style=\"color: #000000;\">Therefore, &#8211; 4a<sup>2<\/sup>\u00a0+ 4ab &#8211; 4ca = -(2 \u00d7 2 \u00d7 a \u00d7 a) + (2 \u00d7 2 \u00d7 a \u00d7 b) &#8211; (2 \u00d7 2 \u00d7 c \u00d7 a)<\/span><br \/>\n<span style=\"color: #000000;\">= 2 \u00d7 2 \u00d7 a (-a\u00a0+ b &#8211; c)<\/span><br \/>\n<span style=\"color: #000000;\">= 4a(-a + b &#8211; c)<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(ix)\u00a0x<sup>2<\/sup>yz + xy<sup>2<\/sup>z + xyz<sup>2<br \/>\n<\/sup><\/strong>x<sup>2<\/sup>yz = x \u00d7 x \u00d7 y \u00d7 z<\/span><br \/>\n<span style=\"color: #000000;\">xy<sup>2<\/sup>z= x \u00d7 y \u00d7 y \u00d7 z<\/span><br \/>\n<span style=\"color: #000000;\">xyz<sup>2<\/sup>\u00a0= x \u00d7 y \u00d7 z \u00d7 z<\/span><br \/>\n<span style=\"color: #000000;\">The common factors are x, y, and z.<\/span><br \/>\n<span style=\"color: #000000;\">Therefore, x<sup>2<\/sup>yz + xy<sup>2<\/sup>z + xyz<sup>2<\/sup>\u00a0= (x \u00d7 x \u00d7 y \u00d7 z) + (x \u00d7 y \u00d7 y \u00d7 z) + (x \u00d7 y \u00d7 z \u00d7 z)<\/span><br \/>\n<span style=\"color: #000000;\">= x \u00d7 y \u00d7 z (x + y + z)<\/span><br \/>\n<span style=\"color: #000000;\">= xyz(x + y + z)<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(x)\u00a0ax<sup>2<\/sup>y + bxy<sup>2<\/sup>\u00a0+ cxyz<br \/>\n<\/strong>ax<sup>2<\/sup>y= a \u00d7 x \u00d7 x \u00d7 y<\/span><br \/>\n<span style=\"color: #000000;\">bxy<sup>2<\/sup>\u00a0= b \u00d7 x \u00d7 y \u00d7 y<\/span><br \/>\n<span style=\"color: #000000;\">cxyz= c \u00d7 x \u00d7 y \u00d7 z<\/span><br \/>\n<span style=\"color: #000000;\">The common factors are x and y.<\/span><br \/>\n<span style=\"color: #000000;\">Therefore, <\/span><br \/>\n<span style=\"color: #000000;\">ax<sup>2<\/sup>y + bxy<sup>2<\/sup>\u00a0+ cxyz = (a \u00d7 x \u00d7 x \u00d7 y) + (b \u00d7 x \u00d7 y \u00d7 y) + (c \u00d7 x \u00d7 y \u00d7 z)<\/span><br \/>\n<span style=\"color: #000000;\">= (x \u00d7 y)[(a \u00d7 x) + (b \u00d7 y) + (c \u00d7 z)]<\/span><br \/>\n<span style=\"color: #000000;\">= xy(ax + by + cz)<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>3. Factorise.<br \/>\n<\/strong><strong>(i)<\/strong> x<sup>2 <\/sup>+ xy + 8x + 8y<br \/>\n<strong>(ii)<\/strong> 15xy \u2013 6x + 5y \u2013 2<br \/>\n<strong>(iii)<\/strong> ax + bx \u2013 ay \u2013 by<br \/>\n<strong>(iv)<\/strong> 15pq + 15 + 9q + 25p<br \/>\n<strong>(v)<\/strong> z \u2013 7 + 7xy \u2013 xyz<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(i) x<sup>2<\/sup> + xy + 8x + 8y <\/strong><\/span><br \/>\n<span style=\"color: #000000;\">= x \u00d7 x + x \u00d7 y + 8 \u00d7 x + 8 \u00d7 y<\/span><br \/>\n<span style=\"color: #000000;\">= x(x + y) + 8(x + y)<\/span><br \/>\n<span style=\"color: #000000;\">= (x + y) (x + 8)<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(ii) 15xy &#8211; 6x + 5y &#8211; 2<br \/>\n<\/strong>= 3 \u00d7 5 \u00d7 x \u00d7 y &#8211; 3 \u00d7 2 \u00d7 x + 5 \u00d7 y &#8211; 2<\/span><br \/>\n<span style=\"color: #000000;\">= 3x (5y &#8211; 2) + 1(5y &#8211; 2)<\/span><br \/>\n<span style=\"color: #000000;\">= (5y &#8211; 2) (3x + 1)<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(iii) ax + bx &#8211; ay &#8211; by<br \/>\n<\/strong>= a \u00d7 x + b \u00d7 x &#8211; a \u00d7 y &#8211; b \u00d7 y<\/span><br \/>\n<span style=\"color: #000000;\">= x(a + b) &#8211; y(a + b)<\/span><br \/>\n<span style=\"color: #000000;\">= (a + b)(x &#8211; y)<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(iv) 15pq + 15 + 9q + 25 p<br \/>\n<\/strong>= 15pq + 9q + 25p + 15<\/span><br \/>\n<span style=\"color: #000000;\">= 3 \u00d7 5 \u00d7 p \u00d7 q + 3 \u00d7 3 \u00d7 q + 5 \u00d7 5 \u00d7 p + 3 \u00d7 5<\/span><br \/>\n<span style=\"color: #000000;\">= 3q(5p + 3) + 5(5p + 3)<\/span><br \/>\n<span style=\"color: #000000;\">= (5p + 3)(3q + 5)<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(v) z &#8211; 7 + 7xy &#8211; xyz<br \/>\n<\/strong>= z &#8211; xyz &#8211; 7 + 7xy<\/span><br \/>\n<span style=\"color: #000000;\">= z &#8211; x \u00d7 y \u00d7 z &#8211; 7 + 7 \u00d7 x \u00d7 y<\/span><br \/>\n<span style=\"color: #000000;\">= z(1- xy) &#8211; 7(1 &#8211; xy)<\/span><br \/>\n<span style=\"color: #000000;\">= (1 &#8211; xy)(z &#8211; 7)<\/span><\/p>\n<p>&nbsp;<\/p>\n<table style=\"width: 100%; border-collapse: collapse;\" border=\"1\">\n<tbody>\n<tr style=\"height: 32px;\">\n<td style=\"width: 100%; background-color: #f2e079; text-align: center; height: 32px;\"><span style=\"color: #ff0000; font-size: 14pt;\"><strong>NCERT Class 8<sup>th\u00a0<\/sup>Solution\u00a0<\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-english\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 English\u201d (Edit)\">NCERT Solutions Class 8 English<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-hindi\/\" aria-label=\"\u201cNCERT Solutions Class 6 Maths\u201d (Edit)\">NCERT Solutions Class 8 Hindi<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 Maths\u201d (Edit)\">NCERT Solutions Class 8 Mathematics<\/a>\u00a0<\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-sanskrit-ruchira\/\" target=\"_blank\" rel=\"noopener\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\">NCERT Solutions Class 8 Sanskrit<\/span><\/strong><\/span><\/a><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-science\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 Social Science\u201d (Edit)\">NCERT Solutions Class 8 Science<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-social-science\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 Social Science\u201d (Edit)\">NCERT Solutions Class 8 Social Science<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 8 Mathematics\u00a0 Chapter &#8211; 14 (Factorisation)\u00a0 The NCERT Solutions in English Language for Class 8 Mathematics Chapter &#8211; 14 Factorisation\u00a0 Exercise 14.1 has been provided here to help the students in solving the questions from this exercise.\u00a0 Chapter 14: Factorisation NCERT Solution Class 8 Maths Ex &#8211; 14.2 NCERT Solution Class 8 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[442],"tags":[470,471,445,5],"class_list":["post-3410","post","type-post","status-publish","format-standard","hentry","category-class-8-maths","tag-ncert-class-8-maths-chapter-14-factorisation-in-english","tag-ncert-solutions-class-8-maths-chapter-14-in-english","tag-ncert-solutions-class-8-maths-in-english","tag-ncert-solutions-in-english"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.9 (Yoast SEO v27.3) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>NCERT Solutions Class 8 Maths Chapter 14 Factorisation Ex 14.1 | TheExamPillar NCERT<\/title>\n<meta name=\"description\" content=\"NCERT Solutions Class 8 Mathematics\u00a0Chapter - 14 (Factorisation)\u00a0The NCERT Solutions in English Language for Class 8 Mathematics Chapter - 14 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