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

Answer :

(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=2x2

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

Answer :

(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.

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

Answer :

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

= x (x + y) + 8 (x + y)

= (x + y) (x + 8)

(ii) 15xy - 6x + 5y - 2 = 3 x 5 x x x y - 3 x 2 x x + 5 x y - 2
= 3x (5y - 2) + 1 (5y - 2)

= (5y - 2) (3x + 1)

(iii) ax + bx - ay - by = a x x + b x x - a x y - b x y

= x (a + b) - y (a + b)

= (a + b) (x - y)

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

=3x5xpxq+3x3xq+5x5xp+3x5

= 3q (5p + 3) + 5 (5p + 3)

= (5p + 3) (3q + 5)

(v) z - 7 + 7xy - xyz = z - x x y x z - 7 + 7 x x x y

= z (1 - xy) - 7 (1 - xy)

= (1 - xy) (z - 7)
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

Answer :

(i) a2 + 8a + 16 = (a)2 + 2 x a x 4 + (4)2

= (a + 4)2 [(x + y)2 = x2 + 2xy + y2]

(ii) p2 - 10p + 25 = (p)2 - 2 x p x 5 + (5)2

= (p - 5)2 [(a - b)2 = a2 - 2ab + b2]

(iii) 25m2 + 30m + 9 = (5m)2 + 2 x 5m x 3 + (3)2

= (5m + 3)2 [(a + b)2 = a2 + 2ab + b2]

(iv) 49y2 + 84yz + 36z2 = (7y)2 + 2 x (7y) x (6z) + (6z)2

= (7y + 6z)2 [(a + b)2 = a2 + 2ab + b2]

(v) 4x2 - 8x + 4 = (2x)2 - 2 (2x) (2) + (2)2

= (2x - 2)2 [(a - b)2 = a2 - 2ab + b2]

= [(2) (x - 1)]2 = 4(x - 1)2

(vi) 121b2 - 88bc + 16c2 = (11b)2 - 2 (11b) (4c) + (4c)2

= (11b - 4c)2 [(a - b)2 = a2 - 2ab + b2]

(vii) (l + m)2 - 4lm = l2 + 2lm + m2 - 4lm

= l2 - 2lm + m2

= (l - m)2 [(a - b)2 = a2 - 2ab + b2]

(viii) a4 + 2a2b2 + b4 = (a2)2 + 2 (a2) (b2) + (b2)2

= (a2 + b2)2 [(a + b)2 = a2 + 2ab + b2]

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

Answer :

(i) 4p2 - 9q2 = (2p)2 - (3q)2

= (2p + 3q) (2p - 3q) [a2 - b2 = (a - b) (a + b)]

(ii) 63a2 - 112b2 = 7(9a2 - 16b2)

= 7[(3a)2 - (4b)2]

= 7(3a + 4b) (3a - 4b) [a2 - b2 = (a - b) (a + b)]

(iii) 49x2 - 36 = (7x)2 - (6)2

= (7x - 6) (7x + 6) [a2 - b2 = (a - b) (a + b)]

(iv) 16x5 - 144x3 = 16x3(x2 - 9)

= 16 x3 [(x)2 - (3)2]

= 16 x3(x - 3) (x + 3) [a2 - b2 = (a - b) (a + b)]

(v) (l + m)2 - (l - m)2 = [(l + m) - (l - m)] [(l + m) + (l - m)]

[Using identity a2 - b2 = (a - b) (a + b)]

= (l + m - l + m) (l + m + l - m)

= 2m x 2l

= 4ml

= 4lm

(vi) 9x2y2 - 16 = (3xy)2 - (4)2

= (3xy - 4) (3xy + 4) [a2 - b2 = (a - b) (a + b)]

(vii) (x2 - 2xy + y2) - z2 = (x - y)2 - (z)2 [(a - b)2 = a2 - 2ab + b2]

= (x - y - z) (x - y + z) [a2 - b2 = (a - b) (a + b)]
(viii) 25a2 - 4b2 + 28bc - 49c2 = 25a2 - (4b2 - 28bc + 49c2)

= (5a)2 - [(2b)2 - 2 x 2b x 7c + (7c)2]

= (5a)2 - [(2b - 7c)2]

[Using identity (a - b)2 = a2 - 2ab + b2]

= [5a + (2b - 7c)] [5a - (2b - 7c)]

[Using identity a2 - b2 = (a - b) (a + b)]

= (5a + 2b - 7c) (5a - 2b + 7c)

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

Answer :
(i) ax2 + bx = a x x x x + b x x = x(ax + b)

(ii) 7p2 + 21q2 = 7 x p x p + 3 x 7 x q x q = 7(p2 + 3q2)

(iii) 2x3 + 2xy2 + 2xz2 = 2x(x2 + y2 + z2)

(iv) am2 + bm2 + bn2 + an2 = am2 + bm2 + an2 + bn2

= m2(a + b) + n2(a + b)

= (a + b) (m2 + n2)

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

= m(l + 1) + 1(l + 1)

= (l + l) (m + 1)

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

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

= 5y(y - 4) + 2z(y - 4)

= (y - 4) (5y + 2z)

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

= 5b(2a + 1) + 2(2a + 1)

= (2a + 1) (5b + 2)

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

= 3x(2y - 3) - 2(2y - 3)

= (2y - 3) (3x - 2)

Q4 :
Factorise

(i) a4 - b4

(ii) p4 - 81

(iii) x4 - (y + z)4

(iv) x4 - (x - z)4

(v) a4 - 2a2b2 + b4

Answer :

(i) a4 - b4 = (a2)2 - (b2)2

= (a2 - b2) (a2 + b2)

= (a - b) (a + b) (a2 + b2)

(ii) p4 - 81 = (p2)2 - (9)2

= (p2 - 9) (p2 + 9)

= [(p)2 - (3)2] (p2 + 9)

= (p - 3) (p + 3) (p2 + 9)

(iii) x4 - (y + z)4 = (x2)2 - [(y +z)2]2

= [x2 - (y + z)2] [x2 + (y + z)2]

= [x - (y + z)][ x + (y + z)] [x2 + (y + z)2]

= (x - y - z) (x + y + z) [x2 + (y + z)2]
(iv) x4 - (x - z)4 = (x2)2 - [(x - z)2]2

= [x2 - (x - z)2] [x2 + (x - z)2]

= [x - (x - z)] [x + (x - z)] [x2 + (x - z)2]

= z(2x - z) [x2 + x2 - 2xz + z2]

= z(2x - z) (2x2 - 2xz + z2)

(v) a4 - 2a2b2 + b4 = (a2)2 - 2 (a2) (b2) + (b2)2

= (a2 - b2)2

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

= (a - b)2 (a + b)2

Q5 :

Factorise the following expressions

(i) p2 + 6p + 8

(ii) q2 - 10q + 21

(iii) p2 + 6p - 16

Answer :

(i) p2 + 6p + 8

It can be observed that, 8 = 4 x 2 and 4 + 2 = 6

p2 + 6p + 8 = p2 + 2p + 4p + 8

= p(p + 2) + 4(p + 2)

= (p + 2) (p + 4)

(ii) q2 - 10q + 21
It can be observed that, 21 = (-7) x (-3) and (-7) + (-3) = - 10

q2 - 10q + 21 = q2 - 7q - 3q + 21

= q(q - 7) - 3(q - 7)

= (q - 7) (q - 3)

(iii) p2 + 6p - 16

It can be observed that, 16 = (-2) x 8 and 8 + (-2) = 6

p2 + 6p - 16 = p2 + 8p - 2p - 16

= p(p + 8) - 2(p + 8)

= (p + 8) (p - 2)

Exercise 14.3 : Solutions of Questions on Page Number : 227

Q1 :

Carry out the following divisions.

(i) 28x4 ÷ 56x

(ii) -36y3 ÷ 9y2

(iii) 66pq2r3 ÷ 11qr2

(iv) 34x3y3z3 ÷ 51xy2z3

(v) 12a8b8 ÷ (-6a6b4)

Answer :

(i) 28x4 = 2 × 2 × 7 × x × x × x × x
56x = 2 × 2 × 2 × 7 × x

(ii) 36y3 = 2 × 2 × 3 × 3 × y × y × y

9y2 = 3 × 3 × y × y

(iii) 66 pq2 r3 = 2 × 3 × 11 × p × q × q × r × r × r

11qr2 = 11 × q × r × r

(iv) 34 x3y3z3 = 2 × 17 × x × x × x × y × y × y × z × z × z

51 xy2z3 = 3 ×17 × x × y × y ×z × z × z

(v) 12a8b8 = 2 × 2 × 3 × a8 × b8

6a6b4 = 2 × 3 × a6 × b4

= - 2a2b4

Q2 :

Divide the given polynomial by the given monomial.

(i) (5x2 - 6x) ÷ 3x

(ii) (3y8 - 4y6 + 5y4) ÷ y4

(iii) 8(x3y2z2 + x2y3z2 + x2y2z3) ÷ 4x2y2z2

(iv) (x3 + 2x2 + 3x) ÷ 2x

(v) (p3q6 - p6q3) ÷ p3q3

Answer :

(i) 5x2 - 6x = x(5x - 6)

(ii) 3y8 - 4y6 + 5y4 = y4(3y4 - 4y2 + 5)

(iii) 8(x3y2z2 + x2y3z2 + x2y2z3) = 8x2y2z2(x + y + z)

(iv) x3 + 2x2 + 3x = x(x2 + 2x + 3)

(v) p3q6 - p6q3 = p3q3(q3 - p3)

Q3 :

Work out the following divisions.

(i) (10x - 25) ÷ 5

(ii) (10x - 25) ÷ (2x - 5)

(iii) 10y(6y + 21) ÷ 5(2y + 7)

(iv) 9x2y2(3z - 24) ÷ 27xy(z - 8)

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

Answer :

(i)

(ii)

(iii)

(iv)

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

Q4 :

Divide as directed.

(i) 5(2x + 1) (3x + 5) ÷ (2x + 1)

(ii) 26xy(x + 5) (y - 4) ÷ 13x(y - 4)

(iii) 52pqr (p + q) (q + r) (r + p) ÷ 104pq(q + r) (r + p)

(iv) 20(y + 4) (y2 + 5y + 3) ÷ 5(y + 4)

(v) x(x + 1) (x + 2) (x + 3) ÷ x(x + 1)

Answer :

(i) = 5(3x + 1)

(ii) = 2y (x + 5)

(iii) 52pqr (p + q) (q + r) (r + p) ÷ 104pq (q + r) (r + p)

(iv) 20(y + 4) (y2 + 5y + 3) = 2 × 2 × 5 × (y + 4) (y2 + 5y + 3)

(v)
= (x + 2) (x + 3)

Q5 :

Factorise the expressions and divide them as directed.

(i) (y2 + 7y + 10) ÷ (y + 5)

(ii) (m2 - 14m - 32) ÷ (m + 2)

(iii) (5p2 - 25p + 20) ÷ (p - 1)

(iv) 4yz(z2 + 6z - 16) ÷ 2y(z + 8)

(v) 5pq(p2 - q2) ÷ 2p(p + q)

(vi) 12xy(9x2 - 16y2) ÷ 4xy(3x + 4y)

(vii) 39y3(50y2- 98) ÷ 26y2(5y+ 7)

Answer :

(i) (y2 + 7y + 10) = y2 + 2y + 5y + 10

= y (y + 2) + 5 (y + 2)

= (y + 2) (y + 5)

(ii) m2 - 14m - 32 = m2 + 2m - 16m - 32

= m (m + 2) - 16 (m + 2)

= (m + 2) (m - 16)
(iii) 5p2 - 25p + 20 = 5(p2 - 5p + 4)

= 5[p2 - p - 4p + 4]

= 5[p(p - 1) - 4(p - 1)]

= 5(p - 1) (p - 4)

(iv) 4yz(z2 + 6z - 16) = 4yz [z2 - 2z + 8z - 16]

= 4yz [z(z - 2) + 8(z - 2)]

= 4yz(z - 2) (z + 8)

(v) 5pq(p2 - q2) = 5pq (p - q) (p + q)

(vi) 12xy(9x2 - 16y2) = 12xy[(3x)2 - (4y)2] = 12xy(3x - 4y) (3x + 4y)

(vii) 39y3(50y2 - 98) = 3 × 13 × y × y × y × 2[(25y2 - 49)]

= 3 × 13 × 2 × y × y × y × [(5y)2 - (7)2]

= 3 × 13 × 2 × y × y × y (5y - 7) (5y + 7)

26y2(5y + 7) = 2 × 13 × y × y × (5y + 7)
39y3(50y2 - 98) ÷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

Answer :

L.H.S. = 4(x - 5) = 4 x x - 4 x 5 = 4x - 20 ≠ R.H.S.

The correct statement is 4(x - 5) = 4x - 20

Q2 :

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

Answer :

L.H.S. = x(3x + 2) = x x 3x + x x 2 = 3x2 + 2x ≠ R.H.S.

The correct statement is x(3x + 2) = 3x2 + 2x

Q3 :

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

Answer :

L.H.S = 2x + 3y ≠ R.H.S.

The correct statement is 2x + 3y = 2x + 3y

Q4 :

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

L.H.S = x + 2x + 3x =1x + 2x + 3x = x(1 + 2 + 3) = 6x ≠ R.H.S.

The correct statement is x + 2x + 3x = 6x

Q5 :

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

Answer :

L.H.S. = 5y + 2y + y - 7y = 8y - 7y = y ≠ R.H.S

The correct statement is 5y + 2y + y - 7y = y

Q6 :

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

Answer :

L.H.S. = 3x + 2x = 5x ≠ R.H.S
The correct statement is 3x + 2x = 5x

Q7 :

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

Answer :

L.H.S = (2x)2 + 4(2x) + 7 = 4x2 + 8x + 7 ≠ R.H.S

The correct statement is (2x)2 + 4(2x) + 7 = 4x2 + 8x + 7

Q8 :

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

Answer :

L.H.S = (2x)2 + 5x = 4x2 + 5x ≠ R.H.S.

The correct statement is (2x)2 + 5x = 4x2 + 5x

Q9 :

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

Answer :

L.H.S. = (3x + 2)2 = (3x)2 + 2(3x)(2) + (2)2 [(a + b)2 = a2 + 2ab + b2]

= 9x2 + 12x + 4 ≠ R.H.S

The correct statement is (3x + 2)2 = 9x2 + 12x + 4

Q10 :

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

Answer :

L.H.S = (y - 3)2 = (y)2 - 2(y)(3) + (3)2 [(a - b)2 = a2 - 2ab + b2]

= y2 - 6y + 9 ≠ R.H.S

The correct statement is (y - 3)2 = y2 - 6y + 9

Q11 :

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

Answer :

L.H.S = (z + 5)2 = (z)2 + 2(z)(5) + (5)2 [(a + b)2 = a2 + 2ab + b2]

= z2 + 10z + 25 ≠ R.H.S

The correct statement is (z + 5)2 = z2 + 10z + 25

Q12 :

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

Answer :
L.H.S. = (2a + 3b) (a - b) = 2a x a + 3b x a - 2a x b - 3b x b

= 2a2 + 3ab - 2ab - 3b2 = 2a2 + ab - 3b2 ≠ R.H.S.

The correct statement is (2a + 3b) (a - b) = 2a2 + ab - 3b2

Q13 :

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

Answer :

L.H.S. = (a + 4) (a + 2) = (a)2 + (4 + 2) (a) + 4 x 2

= a2 + 6a + 8 ≠ R.H.S

The correct statement is (a + 4) (a + 2) = a2 + 6a + 8

Q14 :

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

Answer :

L.H.S. = (a - 4) (a - 2) = (a)2 + [(- 4) + (- 2)] (a) + (- 4) (- 2)

= a2 - 6a + 8 ≠ R.H.S.

The correct statement is (a - 4) (a - 2) = a2 - 6a + 8

Q15 :
Find and correct the errors in the statement:

Answer :

L.H.S =

The correct statement is

Q16 :

Find and correct the errors in the statement:

Answer :

The correct statement is

Q17 :

Find and correct the errors in the statement:

Answer :
L.H.S =

The correct statement is

Q18 :

Find and correct the errors in the statement:

Answer :

L.H.S. = ≠ R.H.S.

The correct statement is

Q19 :

Find and correct the errors in the statement:

Answer :

L.H.S. =

The correct statement is

Q20 :
Find and correct the errors in the statement:

Answer :

L.H.S. =

The correct statement is