RD Sharma Solutions for Class 8 Math Chapter 7 - Factorization (Part-3) | RD Sharma Solutions for Class 8 Mathematics PDF Download

Question 1: Factorize each of the following algebraic expressions:
6x(2x − y) + 7y(2x − y)
Answer 1: 6x(2x−y)+7y(2x−y) 
= (6x+7y)(2x−y)         [Taking (2x−y) as the common factor] 
Question 2:Factorize each of the following algebraic expressions:
2r(y − x) + s(x − y) 
Answer 2: 2r(y−x)+s(x−y)
=2r(y−x)−s(y−x)      [∵(x−y)=−(y−x)] 
=(2r−s)(y−x)              [Taking (y−x) as the common factor] 

Question 3: Factorize each of the following algebraic expressions:
7a(2x − 3) + 3b(2x − 3) 
Answer 3: 7a(2x−3)+3b(2x−3) 
=(7a+3b)(2x−3)            [Taking (2x−3) as the common factor]
Question 4: Factorize each of the following algebraic expressions:
9a(6a − 5b) −12a²(6a − 5b)
Answer 4: 9a(6a−5b)−12a2(6a−5b) 
=(9a−12a2)(6a−5b)     [Taking (6a−5b) as the common factor] 
=3a(3−4a)(6a−5b)       [Taking 3a as the common factor of the quadratic (9a−12a2)

Question 5: Factorize each of the following algebraic expressions:
5(x − 2y)² + 3(x − 2y) 
Answer 5: 5(x−2y)2+3(x−2y)
=[5(x−2y)+3](x−2y)     [Taking (x−2y) as the common factor] (5x−10y+3)(x−2y)

Question 6: Factorize each of the following algebraic expressions: 
16(2l − 3m)² −12(3m − 2l) 
Answer 6: 16(2l−3m)2−12(3m−2l) 
=16(2l−3m)2+12(2l−3m)            [∵(3m−2l)=−(2l−3m)] 
= [16(2l−3m)+12](2l−3m)           [Taking (2l−3m) as the common factor] 
=4[4(2l−3m)+3](2l−3m)              {Taking 4 as the common factor of [16(2l−3m)+12]} 
=4(8l−12m+3)(2l−3m) 
Question 7: Factorize each of the following algebraic expressions: 
3a(x − 2y) −b(x − 2y) 
Answer 7: 3a(x−2y)−b(x−2y) 
=(3a−b)(x−2y)           [Taking (x−2y) as the common factor] 

Question 8: Factorize each of the following algebraic expressions: 
a²(x + y) +b²(x + y) +c²(x + y) 
Answer 8: a2(x+y)+b2(x+y)+c2(x+y) 
=(a2+b2+c2)(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)   [Taking (x−y) as the common factor] 
= (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+2b)−4(a+2b)2 
=[6−4(a+2b)](a+2b)      [Taking (a+2b) as the common factor] 
= 2[3−2(a+2b)](a+2b)   {Taking 2 as the common factor of [6−4(a+2b)]} 
=2(3−2a−4b)(a+2b) 
Question 11: Factorize each of the following algebraic expressions:
a(x − y) + 2b(y − x) + c(x − y)² 
Answer 11: a(x−y)+2b(y−x)+c(x−y)2 
=a(x−y)−2b(x−y)+c(x−y)2   [∵(y−x)=−(x−y)] 
= [a−2b+c(x−y)](x−y) 
= (a−2b+cx−cy)(x−y) 
Question 12: Factorize each of the following algebraic expressions:
−4(x − 2y)² + 8(x −2y) 
Answer 12: −4(x−2y)2+8(x−2y) 
= [−4(x−2y)+8](x−2y)   [Taking (x−2y) as the common factor] 
= 4[−(x−2y)+2](x−2y)   {Taking 4 as the common factor of [−4(x−2y)+8]} 
= 4(2y−x+2)(x−2y) 
Question 13: Factorize each of the following algebraic expressions:
x³(a − 2b) + x²(a − 2b)
Answer 13: x3(a−2b)+x2(a−2b) 
=(x3+x2)(a−2b)       [Taking (a−2b) as the common factor] 
= x2(x+1)(a−2b)      [Taking x2 as the common factor of (x3+x2)]
Question 14: Factorize each of the following algebraic expressions:

(2x − 3y)(a + b) + (3x − 2y)(a + b) 
Answer 14: (2x−3y)(a+b)+(3x−2y)(a+b) 
=(2x−3y+3x−2y)(a+b)   [Taking (a+b) as the common factor] 
=(5x−5y)(a+b) 
=5(x−y)(a+b)                      [Taking 5 as the common factor of (5x−5y)]
Question 15: Factorize each of the following algebraic expressions: 
4(x + y) (3a − b) +6(x + y) (2b − 3a) 
Answer 15: 4(x+y)(3a−b)+6(x+y)(2b−3a)

=2(x+y)[2(3a−b)+3(2b−3a)]                {Taking [2 (x+y)] as the common factor} 
=2(x+y)(6a−2b+6b−9a) 
=2(x+y)(4b−3a)