Question

prove that (x+y)^3 +(y+z)^3 + (z+x)^3 - 3(x+y)(y+z)(z+x) = 2(x^3+y^3+z^3-3xyz)

Answer 1

Are you trying to find a more clever or shorter way than just expanding everything out?

Answer 2

i'm not sure if there is a short way to do this - its a bit tedious to expand everything out but it might be the only way to do it