Question

Show that (a-b)^3+(b-c)^3+(c-a)^3=3(a-b)(b-c)(c-a).

Answer 1

Let x = a-b

y = b-c

z = c-a

For x + y + z = 0

x^3 + y^3 + z^3 = 3 xyz

Since a-b+b-c+c-a = 0

The given equation is satisfied,

Hence,

(a-b)^3+(b-c)^3+(c-a)^3=3(a-b)(b-c)(c-a).