1. The problem statement, all variables and given/known data Prove that if x3+x2y+xy2+y3 = 0, then x = y = 0 or x = -y. 2. Relevant equations N/A 3. The attempt at a solution Assume that x3+x2y+xy2+y3 = 0, in which case, it follows that x3+y3 = -(x2y+xy2) or (x+y)(x2-xy+y2) = -xy(x+y). Equality clearly holds if x+y = 0. Now, suppose that x+y =/= 0, and divide through by x+y. This leaves the equality x2-xy+y2 = -xy or x2+y2 = 0, which can only happen if x = y = 0. Therefore, if x3+x2y+xy2+y3 = 0, then x = -y or x = y = 0. Does this 'proof' work?