Question

Factorize: (a-b) 3 + (b-c) 3 +(c-a)3

Answer 1

(a-b)3 + (b-c)3 + (c-a)3

Let,

a = a-b ; b = b-c; c = c-a


a+b+c = (a-b)+ (b-c) + ( c-a) = 0

therefore,

a3+b3+c3= 3abc

=3(a-b)(b-c)(c-a)