Q. 113.6( 8 Votes )

Factorize each of the following expressions:
(a+b)3-8(a-b)3

Answer :

Given,


(a + b)3 – {2(a – b)}3


= {(a + b) –2(a - b)} { (a+b)2 +4(a-b)2 +2(a+b)(a - b)}  [ By using: x3 - y3 = (x - y)(x2 + y2 +xy)


= (a + b – 2a + 2b)(a2 + b2 + 2ab + 4a2 +4b2 – 8ab + 2a2 – 2b2)


= (3b – a) (7a2 +3b2 - 6ab)

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