Factorize:
a3 + 3a2b + 3ab2 + b3 – 8
We know that,
(a + b)3 = a3 + b3 + 3ab (a + b)
Using this formula, we get
= (a + b)3 – 8
= (a + b)3 – (2)3
We know that,
a3 - b3 = (a - b) (a2 + a × b + b2)
Using this formula, we get
= (a + b – 2) [(a+ b)2 + 2 (a + b) + 4)]