Factorize each of the following expressions:
a3+3a2b3+3ab2+b3-8
Given,
A3+3a2 b+3ab2+b3-8 = (a3 +3a2b +3ab2+b3) – 8
= (a+b)3 -8
= (a+b)3 – (2)3
= (a+b -2) { (a+b)2 + (2)2 + 2(a+b) }
= (a+b - 2) (a2+b2 + 2ab+4+2a+2b)