if W is a non real root of the equation z^3 =1 show that x^3 +y^3 =(x+Wy)[x+(w^2)y](x+y)
i tried multiplying it out but i got no where
If nothing else you can alway find the two complex roots of $z^3-1$ and just substitute them in for $W$ and grind through the algebra.
There is almost certainly a more clever way to go about it but that will solve the problem for you.