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NCERT Solutions for Class 8 Maths Chapter 14 Factorisation

by aglasem
August 28, 2021
in 8th Class
Reading Time: 1 min read
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NCERT Solutions

NCERT Solutions Class 8 Maths Chapter 14 Factorisation – Here are all the NCERT solutions for Class 8 Maths Chapter 14. This solution contains questions, answers, images, explanations of the complete chapter 14 titled Factorisation of Maths taught in class 8. If you are a student of class 8 who is using NCERT Textbook to study Maths, then you must come across chapter 14 Factorisation. After you have studied lesson, you must be looking for answers of its questions. Here you can get complete NCERT Solutions for Class 8 Maths Chapter 14 Factorisation in one place.

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NCERT Solutions Class 8 Maths Chapter 14 Factorisation

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Here on AglaSem Schools, you can access to NCERT Book Solutions in free pdf for Maths for Class 8 so that you can refer them as and when required. The NCERT Solutions to the questions after every unit of NCERT textbooks aimed at helping students solving difficult questions.

For a better understanding of this chapter, you should also see summary of Chapter 14 Factorisation , Maths, Class 8.

Class 8
Subject Maths
Book Mathematics
Chapter Number 14
Chapter Name

Factorisation

NCERT Solutions Class 8 Maths chapter 14 Factorisation

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Class 8, Maths chapter 14, Factorisation solutions are given below in PDF format. You can view them online or download PDF file for future use.

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Question & Answer

Q.1: Factorise: (i) 12x + 36 (ii) 22y – 33z (iii) 14pq + 35pqr

Ans : Missing

Q.2: Find the common factors of the given terms. 
(i) 12x, 36 
(ii) 2y, 22xy 
(iii) \(  14 p q, 28 p^{2} q^{2} \) 
(iv) \(2 x, 3 x^{2}, 4   \) 
(v) \( 6 a b c, 24 a b^{2}, 12 a^{2} b  \) 
(vi) \( 16 x^{3},-4 x^{2}, 32 x  \) 
(vii) \(10 p q, 20 q r, 30 r p  \) 
(viii) \( 3 x^{2} y^{3}, 10 x^{3} y^{2}, 6 x^{2} y^{2} z  \)

Ans : (i) \( 12 x=2 \times 2 \times 3 \times x \) \(36=2 \times 2 \times 3 \times 3 \) The common factors are 2,2,3 And \(2 \times 2 \times 3=12 \) (ii) \(2 y=2 \times y \) \( 22 x y=2 \times 11 \times x \times y \) The common Factors are 2,y And \( 2 \times y=2 y \) (iii) \( 14 p q=2 \times 7 \times p \times q \) \( 28 p^{2} q^{2}=2 \times 2 \times 7 \times p \times p \times q \times q \) The common factors are \( 2,7, p, q \) And \(2 \times 7 \times p \times q=14 p q \) (iv) \(2 x=2 \times x \) \(3 x^{2}=3 \times x \times x \) \( 4=2 \times 2\) The common factor is 1 (v) \(6 a b c=2 \times 3 \times a \times b \times c \) \(24 a b^{2}=2 \times 2 \times 2 \times 3 \times a \times b \times b \) \(12 a^{2} b=2 \times 2 \times 3 \times a \times a \times b \) The common factors are \( 2,3, a, b \) And \( 2 \times 3 \times a \times b=6 a b \) (vi) \( 3 x^{2} y^{3}=3 \times x \times x \times y \times y \times y \) \( -4 x^{2}=-1 \times 2 \times 2 \times x \times x \) \( 32 x=2 \times 2 \times 2 \times 2 \times 2 \times x \) The common factors are \( 2,2, x \) And \( 2 \times 5=10 \) (vii) \(10 p q=2 \times 5 \times p \times q \) \( 20 q r=2 \times 2 \times 5 \times q \times r \) \( 30 r p=2 \times 3 \times 5 \times r \times p \) The common factors are \(2,5 \) And 2*5=10 (viii) \(3 x^{2} y^{3}=3 \times x \times x \times y \times y \times y \) \( 10 x^{3} y^{2}=2 \times 5 \times x \times x \times x \times y \times y \) \( 6 x^{2} y^{2} z=2 \times 3 \times x \times x \times y \times y \times z \) The common factors are \( x, x, y, y \) And \( x \times x \times y \times y=x^{2} y^{2} \)

Q.3: Factorise the following expressions. 


(i) \( 7 x-42 \) 
(ii) 6p – 12q 
(iii) \(7 a^{2}+14 a   \) 
(iv) \( -16 z+20 z^{3} \) 
(v) \( 20 /^{2} m+30 \mathrm{alm}  \) 
(vi) \( 5 x^{2} y-15 x y^{2}  \) 
(vii) \(10 a^{2}-15 b^{2}+20 c^{2}   \) 
(viii) \( -4 a^{2}+4 a b-4 c a  \) 
(ix) \(x^{2} y z+x y^{2} z+x y z^{2} \) 
(x) \( a x^{2} y+b x y^{2}+c x y z \)

Ans : (i) \(7 x=7 \times x \) \( 42=2 \times 3 \times 7 \) The common factor is 7 \( \therefore 7 x-42=(7 \times x)-(2 \times 3 \times 7)=7(x-6) \) (ii) \( 6 p=2 \times 3 \times p \) The common factors are 2 and 3. \( 12 q=2 \times 2 \times 3 \times q \) \( \therefore 6 p-12 q=(2 \times 3 \times p)-(2 \times 2 \times 3 \times q) \) \( =2 \times 3[p-(2 \times q)] \) \( =6(p-2 q) \) (iii) \( 14 a=2 \times 7 \times a \) \(\therefore 7 a^{2}+14 a=(7 \times a \times a)+(2 \times 7 \times a) \) \( =7 \times a[a+2]=7 a(a+2) \) (iv) \( 16 z=2 \times 2 \times 2 \times 2 \times z \) \( 20 z^{3}=2 \times 2 \times 5 \times z \times z \times z \) The common factors \(2,2, \text { and } z \) \( \therefore-16 z+20 z^{3}=-(2 \times 2 \times 2 \times 2 \times z)+(2 \times 2 \times 5 \times z \times z \times z) \) \( =(2 \times 2 \times z)[-(2 \times 2)+(5 \times z \times z)] \) \(=4 z\left(-4+5 z^{2}\right) \) (v) \( 20 /^{2} m=2 \times 2 \times 5 \times / \times l \times m \) \( 30 a / m=2 \times 3 \times 5 \times a \times l \times m \) The common factors are 2,5,l and m \( \therefore 20 /^{2} m+30 a / m=(2 \times 2 \times 5 \times I \times l \times m)+(2 \times 3 \times 5 \times a \times / \times m) \) \( =(2 \times 5 \times I \times m)[(2 \times l)+(3 \times a)] \) \(=10 \operatorName{lm}(2 l+3 a) \) (vi) \( 5 x^{2} y=5 \times x \times x \times y \) \(15 x y^{2}=3 \times 5 \times x \times y \times y \) \( =5 \times x \times y[x-(3 \times y)] \) \(=5 x y(x-3 y) \) \( =5 x y(x-3 y) \) (vii) \( 10 a^{2}=2 \times 5 \times a \times a \) \( 15 b^{2}=3 \times 5 \times b \times b \) \( 20 c^{2}=2 \times 2 \times 5 \times c \times c \) The common factor is 5. \( 10 a^{2}-15 b^{2}+20 c^{2}=(2 \times 5 \times a \times a)-(3 \times 5 \times b \times b)+(2 \times 2 \times 5 \times c \times c) \) \(=5[(2 \times \mathrm{a} \times \mathrm{a})-(3 \times b \times b)+(2 \times 2 \times c \times c)] \) \( =5\left(2 a^{2}-3 b^{2}+4 c^{2}\right) \) (viii) \(4 a^{2}=2 \times 2 \times a \times a \) \( 4 a b=2 \times 2 \times a \times b \) \(4 c a=2 \times 2 \times c \times a \) The common factors are 2,2 and a \( \therefore-4 a^{2}+4 a b-4 c a=-(2 \times 2 \times a \times a)+(2 \times 2 \times a \times b)-(2 \times 2 \times c \times a) \) \( =2 \times 2 \times a[-(a)+b-c] \) \( =4 a(-a+b-c) \) (ix) \(x^{2} y z=x \times x \times y \times z \) \( x y^{2} z=x \times y \times y \times z \) \(x y z^{2}=x \times y \times z \times z \) The common factors are \( x, y, \text { and } z \) \( \therefore x^{2} y z+x y^{2} z+x y z^{2}=(x \times x \times y \times z)+(x \times y \times y \times z)+(x \times y \times z \times z) \) \( =x \times y \times z[x+y+z] \) \( =x y z(x+y+z) \) (x) \( a x^{2} y=a \times x \times x \times y \) \( b x y^{2}=b \times x \times y \times y\) \( c x y z=c \times x \times y \times z \) The common factors are x and y \(a x^{2} y+b x y^{2}+c x y z=(a \times x \times x \times y)+(b \times x \times y \times y)+(c \times x \times y \times z) \) \( =(x \times y)[(a \times x)+(b \times y)+(c \times z)] \) \( =x y(a x+b y+c z) \)

Q.4: Factorise 
(i) \( x^{2}+x y+8 x+8 y  \)
(ii) \(  15 x y-6 x+5 y-2 \)
(iii) \( a x+b x-a y-b y  \)
(iv) \(15 p q+15+9 q+25 p   \)
(v) \( z-7+7 x y-x y z  \)

Ans : (i) \(x^{2}+x y+8 x+8 y=x \times x+x \times y+8 \times x+8 \times y \) \( =x(x+y)+8(x+y) \) \( =(x+y)(x+8) \) (ii) \( 15 x y-6 x+5 y-2=3 \times 5 \times x \times y-3 \times 2 \times x+5 \times y-2 \) \( =3 x(5 y-2)+1(5 y-2) \) \( =(5 y-2)(3 x+1) \) (iii) \( a x+b x-a y-b y=a \times x+b \times x-a \times y-b \times y \) \(=x(a+b)-y(a+b) \) \( =(a+b)(x-y) \) (iv) \(15 p q+15+9 q+25 p=15 p q+9 q+25 p+15 \) \( =3 \times 5 \times p \times q+3 \times 3 \times q+5 \times 5 \times p+3 \times 5 \) \( =3 q(5 p+3)+5(5 p+3) \) (v) \( z-7+7 x y-x y z=z-x \times y \times z-7+7 \times x \times y \) \(=z(1-x y)-7(1-x y) \) \(=(1-x y)(z-7) \)

Q.5: Factorise the following expressions 
(i) \( a^{2}+8 a+16  \)
(ii)\( p^{x}-10 p+25  \)
(iii) \( 25 m^{2}+30 m+9  \)
(iv) \(  49 y^{4}+84 y z+36 z^{2} \)
(v) \(4 x^{2}-8 x+4   \)
(vi) \( 121 b^{2}-88 b c+16 c^{2}  \)
(vii) \( (l+m)^{2}-4 I m  \)
(viii) \( a^{4}+2 a^{2} b^{2}+b^{4}  \)

Ans : (i) \( a^{2}+8 a+16=(a)^{2}+2 \times a \times 4+(4)^{2}\) \( =(a+4)^{2}\left[(x+y)^{2}=x^{2}+2 x y+y^{2}\right] \) (ii) \( p^{2}-10 p+25=(p)^{2}-2 \times p \times 5+(5)^{2} \) \( =(p-5)^{2}\left[(a-b)^{2}=a^{2}-2 a b+b^{2}\right] \) (iii) \( 25 m^{2}+30 m+9=(5 m)^{2}+2 \times 5 m \times 3+(3)^{2} \) \( =(5 m+3)^{2}\left[(a+b)^{2}=a^{2}+2 a b+b^{2}\right] \) (iv) \( 49 y^{2}+84 y z+36 z^{2}=(7 y)^{2}+2 \times(7 y) \times(6 z)+(6 z)^{2} \) \( =(7 y+6 z)^{2}\left[(a+b)^{2}=a^{2}+2 a b+b^{2}\right] \) (v) \( 4 x^{2}-8 x+4=(2 x)^{2}-2(2 x)(2)+(2)^{2} \) \( =(2 x-2)^{2}\left[(a-b)^{2}=a^{2}-2 a b+b^{2}\right] \) \( =[(2)(x-1)]^{2}=4(x-1)^{2} \) (vi) \(121 b^{2}-88 b c+16 c^{2}=(11 b)^{2}-2(11 b)(4 c)+(4 c)^{2} \) \( =(11 b-4 c)^{2}\left[(a-b)^{2}=a^{2}-2 a b+b^{2}\right] \) (v) \( 4 x^{2}-8 x+4=(2 x)^{2}-2(2 x)(2)+(2)^{2} \) \( =(2 x-2)^{2}\left[(a-b)^{2}=a^{2}-2 a b+b^{2}\right] \) \( =[(2)(x-1)]^{2}=4(x-1)^{2} \) (vi) \( 121 b^{2}-88 b c+16 c^{2}=(11 b)^{2}-2(11 b)(4 c)+(4 c)^{2} \) \( =(11 b-4 c)^{2}\left[(a-b)^{2}=a^{2}-2 a b+b^{2}\right] \) (vii) \( (I+m)^{2}-4 l m=f^{2}+2 l m+m^{2}-4 l m \) \( =f^{2}-2 l m+m^{2} \) \( =(I-m)^{2}\left[(a-b)^{2}=a^{2}-2 a b+b^{2}\right]\) (viii) \( a^{4}+2 a^{2} b^{2}+b^{4}=\left(a^{2}\right)^{2}+2\left(a^{2}\right)\left(b^{2}\right)+\left(b^{2}\right)^{2} \) \(=\left(a^{2}+b^{2}\right)^{2}\left[(a+b)^{2}=a^{2}+2 a b+b^{2}\right] \)

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