Question

Express (a-b)cube + (b-c)cube + (c-a) cube as a product of its factors.

Answer 1

Answer:

Let A = a-b

B = b-c

and, C = c-a

Clearly, A+B+C = a-b + b-c + c-a = 0

We know that If A+B+C = 0

Then, A³ + B³ + C³ = 3ABC

Hence, (a-b)³+(b-c)³+(c-a)³ = 3(a-b)(b-c)(c-a)