# NCERT Solutions for Class 8 Maths Maths - NCERT Solution Chapter 14

## Factorisation Class 8

### Exercise 14.1 : Solutions of Questions on Page Number : 220

Q1 :

Find the common factors of the terms

(i) 12x, 36

(ii) 2y, 22xy

(iii) 14pq, 28p2q2

(iv) 2x, 3x2, 4

(v) 6abc, 24ab2, 12a2b

(vi) 16x3, -4x2, 32x

(vii) 10pq, 20qr, 30rp

(viii) 3x2y3, 10x3y2, 6x2y2z

(i) 12x = 2 x 2 x 3 x x

36 = 2 x 2 x 3 x 3

The common factors are 2, 2, 3.

And, 2 x 2 x 3 = 12

(ii) 2y = 2 x y

22xy = 2 x 11 x x x y

The common factors are 2, y.

And, 2 x y = 2y

(iii) 14pq = 2 x 7 x p x q

28p2q2 = 2 x 2 x 7 x p x p x q x q

The common factors are 2, 7, p, q.

And, 2 x 7 x p x q = 14pq

(iv) 2x = 2 x x

3x2 = 3 x x x x

4 = 2 x 2

The common factor is 1.

(v) 6abc = 2 x 3 x a x b x c

24ab2 = 2 x 2 x 2 x 3 x a x b x b

12a2b = 2 x 2 x 3 x a x a x b

The common factors are 2, 3, a, b.

And, 2 x 3 x a x b = 6ab

(vi) 16x3 = 2 x 2 x 2 x 2 x x x x x x

-4x2 = -1 x 2 x 2 x x x x

32x = 2 x 2 x 2 x 2 x 2 x x

The common factors are 2, 2, x.

And, 2 x 2 x x = 4x

(vii) 10pq = 2 x 5 x p x q

20qr = 2 x 2 x 5 x q x r

30rp = 2 x 3 x 5 x r x p

The common factors are 2, 5.

And, 2 x 5 = 10

(viii) 3x2y3 = 3 x x x x x y x y x y

10x3y2 = 2 x 5 x x x x x x x y x y

6x2y2z = 2 x 3 x x x x x y x y x z

The common factors are x, x, y, y.

And,

x x x x y x y = x2y2

Q2 :

Factorise the following expressions

(i) 7x - 42

(ii) 6p - 12q

(iii) 7a2 + 14a

(iv) -16z + 20z3

(v) 20l2m + 30 alm

(vi) 5x2y - 15xy2

(vii) 10a2 - 15b2 + 20c2

(viii) -4a2 + 4ab - 4 ca

(ix) x2yz + xy2z + xyz2

(x) ax2y + bxy2 + cxyz

(i) 7x = 7 x x

42 = 2 x 3 x 7

The common factor is 7.

∴ 7x - 42 = (7 x x) - (2 x 3 x 7) = 7 (x - 6)

(ii) 6p = 2 x 3 x p

12q = 2 x 2 x 3 x q

The common factors are 2 and 3.

∴ 6p - 12q = (2 x 3 x p) - (2 x 2 x 3 x q)

= 2 x 3 [p - (2 x q)]

= 6 (p - 2q)

(iii) 7a2 = 7 x a x a

14a = 2 x 7 x a

The common factors are 7 and a.

∴ 7a2 + 14a = (7 x a x a) + (2 x 7 x a)

= 7 x a [a + 2] = 7a (a + 2)

(iv) 16z = 2 x 2 x 2 x 2 x z

20z3 = 2 x 2 x 5 x z x z x z

The common factors are 2, 2, and z.

∴ -16z + 20z3 = - (2 x 2 x 2 x 2 x z) + (2 x 2 x 5 x z x z x z)

= (2 x 2 x z) [- (2 x 2) + (5 x z x z)]

= 4z (- 4 + 5z2)

(v) 20l2m = 2 x 2 x 5 x l x l x m

30alm = 2 x 3 x 5 x a x l x m

The common factors are 2, 5, l, and m.

∴ 20l2m + 30alm = (2 x 2 x 5 x l x l x m) + (2 x 3 x 5 x a x l x m)

= (2 x 5 x l x m) [(2 x l) + (3 x a)]

= 10lm (2l + 3a)

(vi) 5x2y = 5 x x x x x y

15xy2 = 3 x 5 x x x y x y

The common factors are 5, x, and y.

∴ 5x2y - 15xy2 = (5 x x x x x y) - (3 x 5 x x x y x y)

= 5 x x x y [x - (3 x y)]

= 5xy (x - 3y)

(vii) 10a2 = 2 x 5 x a x a

15b2 = 3 x 5 x b x b

20c2 = 2 x 2 x 5 x c x c

The common factor is 5.

10a2 - 15b2 + 20c2 = (2 x 5 x a x a) - (3 x 5 x b x b) + (2 x 2 x 5 x c x c)

= 5 [(2 x a x a) - (3 x b x b) + (2 x 2 x c x c)]

= 5 (2a2 - 3b2 + 4c2)

(viii) 4a2 = 2 x 2 x a x a

4ab = 2 x 2 x a x b

4ca = 2 x 2 x c x a

The common factors are 2, 2, and a.

∴ -4a2 + 4ab - 4ca = - (2 x 2 x a x a) + (2 x 2 x a x b) - (2 x 2 x c x a)

= 2 x 2 x a [- (a) + b - c]

= 4a (-a + b - c)

(ix) x2yz = x x x x y x z

xy2z = x x y x y x z

xyz2 = x x y x z x z

The common factors are x, y, and z.

x2yz + xy2z + xyz2 = (x x x x y x z) + (x x y x y x z) + (x x y x z x z)

= x x y x z [x + y + z]

= xyz (x + y + z)

(x) ax2y = a x x x x x y

bxy2 = b x x x y x y

cxyz = c x x x y x z

The common factors are x and y.

a

Q3 :

Factorise

(i) x2 + xy + 8x + 8y

(ii) 15xy - 6x + 5y - 2

(iii) ax + bx - ay - by

(iv) 15pq + 15 + 9q + 25p

(v) z - 7 + 7xy - xyz

### Exercise 14.2 : Solutions of Questions on Page Number : 223

Q1 :

Factorise the following expressions.

(i) a2 + 8a + 16

(ii) p2 - 10p + 25

(iii) 25m2 + 30m + 9

(iv) 49y2 + 84yz + 36z2

(v) 4x2 - 8x + 4

(vi) 121b2 - 88bc + 16c2

(vii) (l + m)2 - 4lm (Hint: Expand (l + m)2 first)

(viii) a4 + 2a2b2 + b4

Q2 :

Factorise

(i) 4p2 - 9q2

(ii) 63a2 - 112b2

(iii) 49x2 - 36

(iv) 16x5 - 144x3

(v) (l + m)2 - (l - m)2

(vi) 9x2y2 - 16

(vii) (x2 - 2xy + y2) - z2

(viii) 25a2 - 4b2 + 28bc - 49c2

Q3 :

Factorise the expressions

(i) ax2 + bx

(ii) 7p2 + 21q2

(iii) 2x3 + 2xy2 + 2xz2

(iv) am2 + bm2 + bn2 + an2

(v) (lm + l) + m + 1

(vi) y(y + z) + 9(y + z)

(vii) 5y2 - 20y - 8z + 2yz

(viii) 10ab + 4a + 5b + 2

(ix) 6xy - 4y + 6 - 9x

Q4 :

Factorise

(i) a4 - b4

(ii) p4 - 81

(iii) x4 - (y + z)4

(iv) x4 - (x - z)4

(v) a4 - 2a2b2 + b4

Q5 :

Factorise the following expressions

(i) p2 + 6p + 8

(ii) q2 - 10q + 21

(iii) p2 + 6p - 16

### Exercise 14.3 : Solutions of Questions on Page Number : 227

Q1 :

Carry out the following divisions.

(i) 28x4 ÃƒÂ· 56x

(ii) -36y3 ÃƒÂ· 9y2

(iii) 66pq2r3 ÃƒÂ· 11qr2

(iv) 34x3y3z3 ÃƒÂ· 51xy2z3

(v) 12a8b8 ÃƒÂ· (-6a6b4)

Q2 :

Divide the given polynomial by the given monomial.

(i) (5x2 - 6x) ÃƒÂ· 3x

(ii) (3y8 - 4y6 + 5y4) ÃƒÂ· y4

(iii) 8(x3y2z2 + x2y3z2 + x2y2z3) ÃƒÂ· 4x2y2z2

(iv) (x3 + 2x2 + 3x) ÃƒÂ· 2x

(v) (p3q6 - p6q3) ÃƒÂ· p3q3

Q3 :

Work out the following divisions.

(i) (10x - 25) ÃƒÂ· 5

(ii) (10x - 25) ÃƒÂ· (2x - 5)

(iii) 10y(6y + 21) ÃƒÂ· 5(2y + 7)

(iv) 9x2y2(3z - 24) ÃƒÂ· 27xy(z - 8)

(v) 96abc(3a - 12)(5b - 30) ÃƒÂ· 144(a - 4) (b - 6)

Q4 :

Divide as directed.

(i) 5(2x + 1) (3x + 5) ÃƒÂ· (2x + 1)

(ii) 26xy(x + 5) (y - 4) ÃƒÂ· 13x(y - 4)

(iii) 52pqr (p + q) (q + r) (r + p) ÃƒÂ· 104pq(q + r) (r + p)

(iv) 20(y + 4) (y2 + 5y + 3) ÃƒÂ· 5(y + 4)

(v) x(x + 1) (x + 2) (x + 3) ÃƒÂ· x(x + 1)

Q5 :

Factorise the expressions and divide them as directed.

(i) (y2 + 7y + 10) ÃƒÂ· (y + 5)

(ii) (m2 - 14m - 32) ÃƒÂ· (m + 2)

(iii) (5p2 - 25p + 20) ÃƒÂ· (p - 1)

(iv) 4yz(z2 + 6z - 16) ÃƒÂ· 2y(z + 8)

(v) 5pq(p2 - q2) ÃƒÂ· 2p(p + q)

(vi) 12xy(9x2 - 16y2) ÃƒÂ· 4xy(3x + 4y)

(vii) 39y3(50y2- 98) ÃƒÂ· 26y2(5y+ 7)

### Exercise 14.4 : Solutions of Questions on Page Number : 228

Q1 :

Find and correct the errors in the statement: 4(x - 5) = 4x - 5

Q2 :

Find and correct the errors in the statement: x(3x + 2) = 3x2 + 2

Q3 :

Find and correct the errors in the statement: 2x + 3y = 5xy

Q4 :

Find and correct the errors in the statement: x + 2x + 3x = 5x

Q5 :

Find and correct the errors in the statement: 5y + 2y + y - 7y = 0

Q6 :

Find and correct the errors in the statement: 3x + 2x = 5x2

Q7 :

Find and correct the errors in the statement: (2x)2 + 4(2x) + 7 = 2x2 + 8x + 7

Q8 :

Find and correct the errors in the statement: (2x)2 + 5x = 4x + 5x = 9x

Q9 :

Find and correct the errors in the statement: (3x + 2)2 = 3x2 + 6x + 4

Q10 :

Find and correct the errors in the statement: (y - 3)2 = y2 - 9

Q11 :

Find and correct the errors in the statement: (z + 5)2 = z2 + 25

Q12 :

Find and correct the errors in the statement: (2a + 3b) (a - b) = 2a2 - 3b2

Q13 :

Find and correct the errors in the statement: (a + 4) (a + 2) = a2 + 8

Q14 :

Find and correct the errors in the statement: (a - 4) (a - 2) = a2 - 8

Q15 :

Find and correct the errors in the statement:

Q16 :

Find and correct the errors in the statement:

Q17 :

Find and correct the errors in the statement:

Q18 :

Find and correct the errors in the statement:

Q19 :

Find and correct the errors in the statement:

Q20 :

Find and correct the errors in the statement: