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.
NCERT Solutions Class 8 Maths Chapter 14 Factorisation
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Class | 8 |
Subject | Maths |
Book | Mathematics |
Chapter Number | 14 |
Chapter Name |
Factorisation |
NCERT Solutions Class 8 Maths chapter 14 Factorisation
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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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