Class 8 Exam > Class 8 Notes > Mathematics (Maths) Class 8 > NCERT Solutions: Factorisation (Exercise 12.1, 12.2, 12.3)
Factorisation (Exercise 12.1, 12.2, 12.3) NCERT Solutions | Mathematics (Maths) Class 8 PDF Download
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Page 1
Exercise 2 1 .1
1. Find the common factors of the terms
i. 12x,36
Ans:
Write the factors of each term separately:
12x 2 2 3 x ? ? ? ?
36 2 2 3 3 ? ? ? ?
The factors that appear in both the lists are the common factors.
Hence, the common factors are 2,2,3.
Multiply the common factors, 2 2 3 12 ? ? ?
ii.2y,22xy
Ans:
Write the factors of each term separately:
2y 2 y ??
22xy 2 11 x y ? ? ? ?
The factors that appear in both the lists are the common factors.
Hence, the common factors are 2, y .
Multiply the common factors, 2 y 2y ?? .
iii.
22
14pq,28p q
Ans:
Write the factors of each term separately:
14pq 2 7 p q ? ? ? ?
22
28p q 2 2 7 p p q q ? ? ? ? ? ? ?
The factors that appear in both the lists are the common factors.
Hence, the common factors are 2,7,p,q .
Multiply the common factors, 2 7 p q 14pq ? ? ? ? .
iv.
2
2x,3x ,4
Ans:
Page 2
Exercise 2 1 .1
1. Find the common factors of the terms
i. 12x,36
Ans:
Write the factors of each term separately:
12x 2 2 3 x ? ? ? ?
36 2 2 3 3 ? ? ? ?
The factors that appear in both the lists are the common factors.
Hence, the common factors are 2,2,3.
Multiply the common factors, 2 2 3 12 ? ? ?
ii.2y,22xy
Ans:
Write the factors of each term separately:
2y 2 y ??
22xy 2 11 x y ? ? ? ?
The factors that appear in both the lists are the common factors.
Hence, the common factors are 2, y .
Multiply the common factors, 2 y 2y ?? .
iii.
22
14pq,28p q
Ans:
Write the factors of each term separately:
14pq 2 7 p q ? ? ? ?
22
28p q 2 2 7 p p q q ? ? ? ? ? ? ?
The factors that appear in both the lists are the common factors.
Hence, the common factors are 2,7,p,q .
Multiply the common factors, 2 7 p q 14pq ? ? ? ? .
iv.
2
2x,3x ,4
Ans:
Write the factors of each term separately:
2x 2 x ??
2
3x 3 x x ? ? ?
4 2 2 ??
The factors that appear in both the lists are the common factors.
Hence, the common factor is 1.
v.
22
6abc,24ab ,12a b
Ans:
Write the factors of each term separately:
6abc 2 3 a b c ? ? ? ? ?
2
24ab 2 2 2 3 a b b ? ? ? ? ? ? ?
2
12a b 2 2 3 a a b ? ? ? ? ? ?
The factors that appear in both the lists are the common factors.
Hence, the common factors are 2,3,a,b .
Multiply the common factors, 2 3 a b 6ab ? ? ? ? .
vi.
32
16x , 4x ,32x ?
Ans:
Write the factors of each term separately:
3
16x 2 2 2 2 x x x ? ? ? ? ? ? ?
2
4x 1 2 2 x x ? ? ? ? ? ? ?
32x 2 2 2 2 2 x ? ? ? ? ? ?
The factors that appear in both the lists are the common factors.
Hence, the common factors are 2,2,x
Multiply the common factors, 2 2 x 4x ? ? ?
vii.10pq,20qr,30rp
Ans:
Write the factors of each term separately:
10pq 2 5 p q ? ? ? ?
20qr 2 2 5 q r ? ? ? ? ?
30rp 2 3 5 r p ? ? ? ? ?
The factors that appear in both the lists are the common factors.
Hence, the common factors are 2,5 .
Multiply the common factors, 2 5 10 ?? .
viii.
2 3 3 2 2 2
3x y ,10x y ,6x y z
Ans:
Page 3
Exercise 2 1 .1
1. Find the common factors of the terms
i. 12x,36
Ans:
Write the factors of each term separately:
12x 2 2 3 x ? ? ? ?
36 2 2 3 3 ? ? ? ?
The factors that appear in both the lists are the common factors.
Hence, the common factors are 2,2,3.
Multiply the common factors, 2 2 3 12 ? ? ?
ii.2y,22xy
Ans:
Write the factors of each term separately:
2y 2 y ??
22xy 2 11 x y ? ? ? ?
The factors that appear in both the lists are the common factors.
Hence, the common factors are 2, y .
Multiply the common factors, 2 y 2y ?? .
iii.
22
14pq,28p q
Ans:
Write the factors of each term separately:
14pq 2 7 p q ? ? ? ?
22
28p q 2 2 7 p p q q ? ? ? ? ? ? ?
The factors that appear in both the lists are the common factors.
Hence, the common factors are 2,7,p,q .
Multiply the common factors, 2 7 p q 14pq ? ? ? ? .
iv.
2
2x,3x ,4
Ans:
Write the factors of each term separately:
2x 2 x ??
2
3x 3 x x ? ? ?
4 2 2 ??
The factors that appear in both the lists are the common factors.
Hence, the common factor is 1.
v.
22
6abc,24ab ,12a b
Ans:
Write the factors of each term separately:
6abc 2 3 a b c ? ? ? ? ?
2
24ab 2 2 2 3 a b b ? ? ? ? ? ? ?
2
12a b 2 2 3 a a b ? ? ? ? ? ?
The factors that appear in both the lists are the common factors.
Hence, the common factors are 2,3,a,b .
Multiply the common factors, 2 3 a b 6ab ? ? ? ? .
vi.
32
16x , 4x ,32x ?
Ans:
Write the factors of each term separately:
3
16x 2 2 2 2 x x x ? ? ? ? ? ? ?
2
4x 1 2 2 x x ? ? ? ? ? ? ?
32x 2 2 2 2 2 x ? ? ? ? ? ?
The factors that appear in both the lists are the common factors.
Hence, the common factors are 2,2,x
Multiply the common factors, 2 2 x 4x ? ? ?
vii.10pq,20qr,30rp
Ans:
Write the factors of each term separately:
10pq 2 5 p q ? ? ? ?
20qr 2 2 5 q r ? ? ? ? ?
30rp 2 3 5 r p ? ? ? ? ?
The factors that appear in both the lists are the common factors.
Hence, the common factors are 2,5 .
Multiply the common factors, 2 5 10 ?? .
viii.
2 3 3 2 2 2
3x y ,10x y ,6x y z
Ans:
Write the factors of each term separately:
23
3x y 3 x x y y y ? ? ? ? ? ?
32
10x y 2 5 x x x y y ? ? ? ? ? ? ?
22
6x y z 2 3 x x y y z ? ? ? ? ? ? ?
The factors that appear in both the lists are the common factors.
Hence, the common factors are 2 7 p q 14pq ? ? ? ? .
2. Factorise the following expressions
i. 7x 42 ?
Ans:
Take out the common factors from all the terms to factorize.
7x 7 x ??
42 2 3 7 ? ? ?
The common factor is 7
7x 42 (7 x) (2 3 7) 7(x 6) ? ? ? ? ? ? ? ? ?
ii. 6p 12q ?
Ans:
Take out the common factors from all the terms to factorize.
6p 2 3 p ? ? ?
12q 2 2 3 q ? ? ? ?
The common factors are 2 and 3.
6p 12q (2 3 p) (2 2 3 q) ? ? ? ? ? ? ? ?
2 3[p (2 q)] ? ? ? ?
6(p 2q) ??
iii.
2
7a 14a ?
Ans:
Take out the common factors from all the terms to factorize.
2
7a 7 a a ? ? ?
14a 2 7 a ? ? ?
The common factors are 7 and a
2
7a 14a (7 a a) (2 7 a) ? ? ? ? ? ? ? ?
7 a[a 2] ? ? ?
7a(a 2) ??
iv.
3
16z 20z ??
Ans:
Page 4
Exercise 2 1 .1
1. Find the common factors of the terms
i. 12x,36
Ans:
Write the factors of each term separately:
12x 2 2 3 x ? ? ? ?
36 2 2 3 3 ? ? ? ?
The factors that appear in both the lists are the common factors.
Hence, the common factors are 2,2,3.
Multiply the common factors, 2 2 3 12 ? ? ?
ii.2y,22xy
Ans:
Write the factors of each term separately:
2y 2 y ??
22xy 2 11 x y ? ? ? ?
The factors that appear in both the lists are the common factors.
Hence, the common factors are 2, y .
Multiply the common factors, 2 y 2y ?? .
iii.
22
14pq,28p q
Ans:
Write the factors of each term separately:
14pq 2 7 p q ? ? ? ?
22
28p q 2 2 7 p p q q ? ? ? ? ? ? ?
The factors that appear in both the lists are the common factors.
Hence, the common factors are 2,7,p,q .
Multiply the common factors, 2 7 p q 14pq ? ? ? ? .
iv.
2
2x,3x ,4
Ans:
Write the factors of each term separately:
2x 2 x ??
2
3x 3 x x ? ? ?
4 2 2 ??
The factors that appear in both the lists are the common factors.
Hence, the common factor is 1.
v.
22
6abc,24ab ,12a b
Ans:
Write the factors of each term separately:
6abc 2 3 a b c ? ? ? ? ?
2
24ab 2 2 2 3 a b b ? ? ? ? ? ? ?
2
12a b 2 2 3 a a b ? ? ? ? ? ?
The factors that appear in both the lists are the common factors.
Hence, the common factors are 2,3,a,b .
Multiply the common factors, 2 3 a b 6ab ? ? ? ? .
vi.
32
16x , 4x ,32x ?
Ans:
Write the factors of each term separately:
3
16x 2 2 2 2 x x x ? ? ? ? ? ? ?
2
4x 1 2 2 x x ? ? ? ? ? ? ?
32x 2 2 2 2 2 x ? ? ? ? ? ?
The factors that appear in both the lists are the common factors.
Hence, the common factors are 2,2,x
Multiply the common factors, 2 2 x 4x ? ? ?
vii.10pq,20qr,30rp
Ans:
Write the factors of each term separately:
10pq 2 5 p q ? ? ? ?
20qr 2 2 5 q r ? ? ? ? ?
30rp 2 3 5 r p ? ? ? ? ?
The factors that appear in both the lists are the common factors.
Hence, the common factors are 2,5 .
Multiply the common factors, 2 5 10 ?? .
viii.
2 3 3 2 2 2
3x y ,10x y ,6x y z
Ans:
Write the factors of each term separately:
23
3x y 3 x x y y y ? ? ? ? ? ?
32
10x y 2 5 x x x y y ? ? ? ? ? ? ?
22
6x y z 2 3 x x y y z ? ? ? ? ? ? ?
The factors that appear in both the lists are the common factors.
Hence, the common factors are 2 7 p q 14pq ? ? ? ? .
2. Factorise the following expressions
i. 7x 42 ?
Ans:
Take out the common factors from all the terms to factorize.
7x 7 x ??
42 2 3 7 ? ? ?
The common factor is 7
7x 42 (7 x) (2 3 7) 7(x 6) ? ? ? ? ? ? ? ? ?
ii. 6p 12q ?
Ans:
Take out the common factors from all the terms to factorize.
6p 2 3 p ? ? ?
12q 2 2 3 q ? ? ? ?
The common factors are 2 and 3.
6p 12q (2 3 p) (2 2 3 q) ? ? ? ? ? ? ? ?
2 3[p (2 q)] ? ? ? ?
6(p 2q) ??
iii.
2
7a 14a ?
Ans:
Take out the common factors from all the terms to factorize.
2
7a 7 a a ? ? ?
14a 2 7 a ? ? ?
The common factors are 7 and a
2
7a 14a (7 a a) (2 7 a) ? ? ? ? ? ? ? ?
7 a[a 2] ? ? ?
7a(a 2) ??
iv.
3
16z 20z ??
Ans:
Take out the common factors from all the terms to factorize.
16z 2 2 2 2 z ? ? ? ? ?
3
20z 2 2 5 z z z ? ? ? ? ? ?
The common factors are 2,2, and z .
3
16z 20z (2 2 2 2 z) (2 2 5 z z z) ? ? ? ? ? ? ? ? ? ? ? ? ? ?
(2 2 z)[ (2 2) (5 z z)] ? ? ? ? ? ? ? ?
? ?
2
4z 4 5z ? ? ?
v.
2
20l m 30alm ?
Ans:
Take out the common factors from all the terms to factorize.
2
20l m 2 2 5 1 1 m ? ? ? ? ? ?
30alm 2 3 5 a 1 m ? ? ? ? ? ?
The common factors are 2,5,1, and m .
2
20l m 30alm (2 2 5 1 1 m) (2 3 5 a 1 m) ? ? ? ? ? ? ? ? ? ? ? ? ? ?
(2 5 1 m)[(2 l) (3 a)] ? ? ? ? ? ? ?
10lm(2l 3a) ??
vi.
22
5x y 15xy ?
Ans:
Take out the common factors from all the terms to factorize.
2
5x y 5 x x y ? ? ? ?
2
15xy 3 5 x y y ? ? ? ? ?
The common factors are5,x , and y.
22
5x y 15xy (5 x x y) (3 5 x y y) ? ? ? ? ? ? ? ? ? ?
5 x y[x (3 y)] ? ? ? ? ?
5xy(x 3y) ??
vii.
2 2 2
10a 15b 20c ??
Ans:
Take out the common factors from all the terms to factorize.
2
10a 2 5 a a ? ? ? ?
2
15b 3 5 b b ? ? ? ?
2
20c 2 2 5 c c ? ? ? ? ?
The common factor is 5
2 2 2
10a 15b 20c (2 5 a a) (3 5 b b) (2 2 5 c c) ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
5[(2 a a) (3 b b) (2 2 c c)] ? ? ? ? ? ? ? ? ? ?
Page 5
Exercise 2 1 .1
1. Find the common factors of the terms
i. 12x,36
Ans:
Write the factors of each term separately:
12x 2 2 3 x ? ? ? ?
36 2 2 3 3 ? ? ? ?
The factors that appear in both the lists are the common factors.
Hence, the common factors are 2,2,3.
Multiply the common factors, 2 2 3 12 ? ? ?
ii.2y,22xy
Ans:
Write the factors of each term separately:
2y 2 y ??
22xy 2 11 x y ? ? ? ?
The factors that appear in both the lists are the common factors.
Hence, the common factors are 2, y .
Multiply the common factors, 2 y 2y ?? .
iii.
22
14pq,28p q
Ans:
Write the factors of each term separately:
14pq 2 7 p q ? ? ? ?
22
28p q 2 2 7 p p q q ? ? ? ? ? ? ?
The factors that appear in both the lists are the common factors.
Hence, the common factors are 2,7,p,q .
Multiply the common factors, 2 7 p q 14pq ? ? ? ? .
iv.
2
2x,3x ,4
Ans:
Write the factors of each term separately:
2x 2 x ??
2
3x 3 x x ? ? ?
4 2 2 ??
The factors that appear in both the lists are the common factors.
Hence, the common factor is 1.
v.
22
6abc,24ab ,12a b
Ans:
Write the factors of each term separately:
6abc 2 3 a b c ? ? ? ? ?
2
24ab 2 2 2 3 a b b ? ? ? ? ? ? ?
2
12a b 2 2 3 a a b ? ? ? ? ? ?
The factors that appear in both the lists are the common factors.
Hence, the common factors are 2,3,a,b .
Multiply the common factors, 2 3 a b 6ab ? ? ? ? .
vi.
32
16x , 4x ,32x ?
Ans:
Write the factors of each term separately:
3
16x 2 2 2 2 x x x ? ? ? ? ? ? ?
2
4x 1 2 2 x x ? ? ? ? ? ? ?
32x 2 2 2 2 2 x ? ? ? ? ? ?
The factors that appear in both the lists are the common factors.
Hence, the common factors are 2,2,x
Multiply the common factors, 2 2 x 4x ? ? ?
vii.10pq,20qr,30rp
Ans:
Write the factors of each term separately:
10pq 2 5 p q ? ? ? ?
20qr 2 2 5 q r ? ? ? ? ?
30rp 2 3 5 r p ? ? ? ? ?
The factors that appear in both the lists are the common factors.
Hence, the common factors are 2,5 .
Multiply the common factors, 2 5 10 ?? .
viii.
2 3 3 2 2 2
3x y ,10x y ,6x y z
Ans:
Write the factors of each term separately:
23
3x y 3 x x y y y ? ? ? ? ? ?
32
10x y 2 5 x x x y y ? ? ? ? ? ? ?
22
6x y z 2 3 x x y y z ? ? ? ? ? ? ?
The factors that appear in both the lists are the common factors.
Hence, the common factors are 2 7 p q 14pq ? ? ? ? .
2. Factorise the following expressions
i. 7x 42 ?
Ans:
Take out the common factors from all the terms to factorize.
7x 7 x ??
42 2 3 7 ? ? ?
The common factor is 7
7x 42 (7 x) (2 3 7) 7(x 6) ? ? ? ? ? ? ? ? ?
ii. 6p 12q ?
Ans:
Take out the common factors from all the terms to factorize.
6p 2 3 p ? ? ?
12q 2 2 3 q ? ? ? ?
The common factors are 2 and 3.
6p 12q (2 3 p) (2 2 3 q) ? ? ? ? ? ? ? ?
2 3[p (2 q)] ? ? ? ?
6(p 2q) ??
iii.
2
7a 14a ?
Ans:
Take out the common factors from all the terms to factorize.
2
7a 7 a a ? ? ?
14a 2 7 a ? ? ?
The common factors are 7 and a
2
7a 14a (7 a a) (2 7 a) ? ? ? ? ? ? ? ?
7 a[a 2] ? ? ?
7a(a 2) ??
iv.
3
16z 20z ??
Ans:
Take out the common factors from all the terms to factorize.
16z 2 2 2 2 z ? ? ? ? ?
3
20z 2 2 5 z z z ? ? ? ? ? ?
The common factors are 2,2, and z .
3
16z 20z (2 2 2 2 z) (2 2 5 z z z) ? ? ? ? ? ? ? ? ? ? ? ? ? ?
(2 2 z)[ (2 2) (5 z z)] ? ? ? ? ? ? ? ?
? ?
2
4z 4 5z ? ? ?
v.
2
20l m 30alm ?
Ans:
Take out the common factors from all the terms to factorize.
2
20l m 2 2 5 1 1 m ? ? ? ? ? ?
30alm 2 3 5 a 1 m ? ? ? ? ? ?
The common factors are 2,5,1, and m .
2
20l m 30alm (2 2 5 1 1 m) (2 3 5 a 1 m) ? ? ? ? ? ? ? ? ? ? ? ? ? ?
(2 5 1 m)[(2 l) (3 a)] ? ? ? ? ? ? ?
10lm(2l 3a) ??
vi.
22
5x y 15xy ?
Ans:
Take out the common factors from all the terms to factorize.
2
5x y 5 x x y ? ? ? ?
2
15xy 3 5 x y y ? ? ? ? ?
The common factors are5,x , and y.
22
5x y 15xy (5 x x y) (3 5 x y y) ? ? ? ? ? ? ? ? ? ?
5 x y[x (3 y)] ? ? ? ? ?
5xy(x 3y) ??
vii.
2 2 2
10a 15b 20c ??
Ans:
Take out the common factors from all the terms to factorize.
2
10a 2 5 a a ? ? ? ?
2
15b 3 5 b b ? ? ? ?
2
20c 2 2 5 c c ? ? ? ? ?
The common factor is 5
2 2 2
10a 15b 20c (2 5 a a) (3 5 b b) (2 2 5 c c) ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
5[(2 a a) (3 b b) (2 2 c c)] ? ? ? ? ? ? ? ? ? ?
? ?
222
5 2a 3b 4c ? ? ?
viii.
2
4a 4ab 4ca ? ? ?
Ans:
Take out the common factors from all the terms to factorize.
2
4a 2 2 a a ? ? ? ?
4ab 2 2 a b ? ? ? ?
4ca 2 2 c a ? ? ? ?
The common factors are 2,2, and a
2
4a 4ab 4ca (2 2 a a) (2 2 a b) (2 2 c a) ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
2 2 a[ (a) b c] ? ? ? ? ? ?
4a( a b c) ? ? ? ?
ix.
2 2 2
x yz xy z xyz ??
Ans:
Take out the common factors from all the terms to factorize.
2
x yz x x y z ? ? ? ?
2
xy z x y y z ? ? ? ?
2
xyz x y z z ? ? ? ?
The common factors are x,y , and z
2 2 2
x yz xy z xyz (x x y z) (x y y z) (x y z z) ? ? ? ? ? ? ? ? ? ? ? ? ? ?
x y z[x y z] ? ? ? ? ?
xyz(x y z) ? ? ?
x.
22
ax y bxy cxyz ??
Ans:
Take out the common factors from all the terms to factorize.
2
ax y a x x y ? ? ? ?
2
bxy b x y y ? ? ? ?
cxyz c x y z ? ? ? ?
The common factors are x and y.
22
ax y bxy cxyz (a x x y) (b x y y) (c x y z) ? ? ? ? ? ? ? ? ? ? ? ? ? ?
(x y)[(a x) (b y) (c z)] ? ? ? ? ? ? ?
xy(ax by cz) ? ? ?
3. Factorise
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NCERT Solutions: Factorisation (Exercise 12.1, 12.2, 12.3) Class 8 Questions
The "NCERT Solutions: Factorisation (Exercise 12.1, 12.2, 12.3) Class 8 Questions" guide is a valuable resource for all aspiring students preparing for the
Class 8 exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.
Study NCERT Solutions: Factorisation (Exercise 12.1, 12.2, 12.3) on the App
Students of Class 8 can study NCERT Solutions: Factorisation (Exercise 12.1, 12.2, 12.3) alongwith tests & analysis from the EduRev app,
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The content of NCERT Solutions: Factorisation (Exercise 12.1, 12.2, 12.3) is prepared as per the latest Class 8 syllabus.
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