myhelper: RD Sharma solution class 8 chapter 7 Factorization Exercise 7.3

Exercise 7.3

Page-7.7

Question 1:

Factorize each of the following algebraic expressions:
6x(2x − y) + 7y(2x − y)

Answer 1:

$6 x (2 x - y) + 7 y (2 x - y) = (6 x + 7 y) (2 x - y) [T a k i n g (2 x - y) a s t h e c o m m o n f a c t o r]$

Question 2:

Factorize each of the following algebraic expressions:
2r(y − x) + s(x − y)

Answer 2:

$2 r (y - x) + s (x - y) = 2 r (y - x) - s (y - x) [∵ (x - y) = - (y - x)] = (2 r - s) (y - x) [T a k i n g (y - x) a s t h e c o m m o n f a c t o r]$

Question 3:

Factorize each of the following algebraic expressions:
7a(2x − 3) + 3b(2x − 3)

Answer 3:

$7 a (2 x - 3) + 3 b (2 x - 3) = (7 a + 3 b) (2 x - 3) [T a k i n g (2 x - 3) a s t h e c o m m o n f a c t o r]$

Question 4:

Factorize each of the following algebraic expressions:
9a(6a − 5b) −12a²(6a − 5b)

Answer 4:

$9 a (6 a - 5 b) - 12 a^{2} (6 a - 5 b) = (9 a - 12 a^{2}) (6 a - 5 b) [T a k i n g (6 a - 5 b) a s t h e c o m m o n f a c t o r] = 3 a (3 - 4 a) (6 a - 5 b) [T a k i n g 3 a a s t h e c o m m o n f a c t o r o f t h e q u a d r a t i c (9 a - 12 a^{2})]$

Question 5:

Factorize each of the following algebraic expressions:
5(x − 2y)² + 3(x − 2y)

Answer 5:

$5 (x - 2 y)^{2} + 3 (x - 2 y) = [5 (x - 2 y) + 3] (x - 2 y) [T a k i n g (x - 2 y) a s t h e c o m m o n f a c t o r] = (5 x - 10 y + 3) (x - 2 y)$

Question 6:

Factorize each of the following algebraic expressions:
16(2l − 3m)² −12(3m − 2l)

Answer 6:

$16 (2 l - 3 m)^{2} - 12 (3 m - 2 l) = 16 (2 l - 3 m)^{2} + 12 (2 l - 3 m) [∵ (3 m - 2 l) = - (2 l - 3 m)] = [16 (2 l - 3 m) + 12] (2 l - 3 m) [T a k i n g (2 l - 3 m) a s t h e c o m m o n f a c t o r] = 4 [4 (2 l - 3 m) + 3] (2 l - 3 m) {T a k i n g 4 a s t h e c o m m o n f a c t o r o f [16 (2 l - 3 m) + 12]} = 4 (8 l - 12 m + 3) (2 l - 3 m)$

Question 7:

Factorize each of the following algebraic expressions:
3a(x − 2y) −b(x − 2y)

Answer 7:

$3 a (x - 2 y) - b (x - 2 y) = (3 a - b) (x - 2 y) [Taking (x - 2 y) as the common factor]$

Question 8:

Factorize each of the following algebraic expressions:
a²(x + y) +b²(x + y) +c²(x + y)

Answer 8:

$a^{2} (x + y) + b^{2} (x + y) + c^{2} (x + y) = (a^{2} + b^{2} + c^{2}) (x + y) [Taking (x + y) as the common factor]$

Question 9:

Factorize each of the following algebraic expressions:
(x − y)² + (x − y)

Answer 9:

$(x - y)^{2} + (x - y) = (x - y) (x - y) + (x - y) [T a k i n g (x - y) a s t h e c o m m o n f a c t o r] = (x - y + 1) (x - y)$

Question 10:

Factorize each of the following algebraic expressions:
6(a + 2b) −4(a + 2b)²

Answer 10:

$6 (a + 2 b) - 4 (a + 2 b)^{2} = [6 - 4 (a + 2 b)] (a + 2 b) [T a k i n g (a + 2 b) a s t h e c o m m o n f a c t o r] = 2 [3 - 2 (a + 2 b)] (a + 2 b) {T a k i n g 2 a s t h e c o m m o n f a c t o r o f [6 - 4 (a + 2 b)]} = 2 (3 - 2 a - 4 b) (a + 2 b)$

Question 11:

Factorize each of the following algebraic expressions:
a(x − y) + 2b(y − x) + c(x − y)²

Answer 11:

$a (x - y) + 2 b (y - x) + c (x - y)^{2} = a (x - y) - 2 b (x - y) + c (x - y)^{2} [∵ (y - x) = - (x - y)] = [a - 2 b + c (x - y)] (x - y) = (a - 2 b + c x - c y) (x - y)$

Question 12:

Factorize each of the following algebraic expressions:
−4(x − 2y)² + 8(x −2y)

Answer 12:

$- 4 (x - 2 y)^{2} + 8 (x - 2 y) = [- 4 (x - 2 y) + 8] (x - 2 y) [T a k i n g (x - 2 y) a s t h e c o m m o n f a c t o r] = 4 [- (x - 2 y) + 2] (x - 2 y) {T a k i n g 4 a s t h e c o m m o n f a c t o r o f [- 4 (x - 2 y) + 8]} = 4 (2 y - x + 2) (x - 2 y)$

Question 13:

Factorize each of the following algebraic expressions:
x³(a − 2b) + x²(a − 2b)

Answer 13:

$x^{3} (a - 2 b) + x^{2} (a - 2 b) = (x^{3} + x^{2}) (a - 2 b) [T a k i n g (a - 2 b) a s t h e c o m m o n f a c t o r] = x^{2} (x + 1) (a - 2 b) [T a k i n g x^{2} a s t h e c o m m o n f a c t o r o f (x^{3} + x^{2})]$

Question 14:

Factorize each of the following algebraic expressions:
(2x − 3y)(a + b) + (3x − 2y)(a + b)

Answer 14:

$(2 x - 3 y) (a + b) + (3 x - 2 y) (a + b) = (2 x - 3 y + 3 x - 2 y) (a + b) [T a k i n g (a + b) a s t h e c o m m o n f a c t o r] = (5 x - 5 y) (a + b) = 5 (x - y) (a + b) [T a k i n g 5 a s t h e c o m m o n f a c t o r o f (5 x - 5 y)]$

Question 15:

Factorize each of the following algebraic expressions:
4(x + y) (3a − b) +6(x + y) (2b − 3a)

Answer 15:

$4 (x + y) (3 a - b) + 6 (x + y) (2 b - 3 a) = 2 (x + y) [2 (3 a - b) + 3 (2 b - 3 a)] {T a k i n g [2 (x + y)] a s t h e c o m m o n f a c t o r} = 2 (x + y) (6 a - 2 b + 6 b - 9 a) = 2 (x + y) (4 b - 3 a)$

RD Sharma solution class 8 chapter 7 Factorization Exercise 7.3