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RD Chapter 5 Factorisation of Algebraic Expressions Ex 5.2 Solutions

Question - 21 : - x3 + 6x2 + 12x + 16

Answer - 21 : -

x3 + 6x2 + 12x + 16
= (x)3 + 3.x2.2 + 3.x.4 + (2)3 +8           {∵ a3 + 3a2b + 3ab2 +b3 =(a + b)3}
= (x + 2)3 + 8 = (x + 2)3 + (2)3
= (x + 2 + 2) [(x + 2)2 – (x + 2) x 2 + (2)2]{∵ a3 +b2 = (a + b) (a2 – ab + b2}
= (x + 4) (x2 + 4x + 4 – 2x – 4 + 4)
= (x + 4) (x2 + 2x + 4)

Question - 22 : -

Answer - 22 : -


Question - 23 : - a_3 + 3a_2b + 3ab_2 + b_3 – 8

Answer - 23 : -

a3 + 3a2b + 3ab2 + b3 –8
= (a + b)3 – (2)3
= (a + b -2)[(a + b)2 + (a +b)x2 + (2)2]
= (a + b-2) (a2 + b2 + 2ab + 2a + 2b + 4)
= (a + b – 2) (a2 + b2 + 2ab + 2(a + b) + 4]
= (a + b – 2) [(a + b)2 + 2(a + b) + 4}

Question - 24 : - 8a3 – b3 – 4ax + 2bx

Answer - 24 : -

8a3 – b3 – 4ax + 2bx
(2a)3 – (b)3 – 2x(2a – b)
= (2a-b)[(2a)2 + 2a x b + (b)2]- 2x(2a-b)
= (2a – b) [4a2 + 2ab + b2] – 2x(2a – b)
= (2a – b) [4a2 + 2ab + b2 – 2x]

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