Factorize:
27a3 – b3 + 8c3 + 18abc
We know that,
a3 + b3 + c3 – 3abc = (a + b + c) (a2 + b2 + c2 – ab – bc – ca)]
Using this formula, we get
= (3a)3 + (-b)3 + (2c)3 – 3 (3a) (-b) (2c)
= [3a + (-b) + 2c] [(3a)2 + (-b)2 + (2c)2 – (3a) (-b) – (-b) (2c) – (2c) (3a)]
= (3a - b + 2c) (9a2 + b2 + 4c2+ 3ab + 2bc – 6ca)