Question

Factorise a³(b-c)³+b³(c-a)³+c³(a-b)³

Answer 1

a³(b-c)³+b³(c-a)³+c³(a-b)³

Let x = a(b-c) , y = b(c-a), z = c(a-b)

Here , x + y + z = 0

Then x³ + y³ + z³ must be equal to 3xyz.

Substitute for x = a(b-c) , y = b(c-a), z = c(a-b) and get the answer.