Factor This

Submitted by Maria Elena Alvarez, 04/04/1997. Original answer by Valerio De Angelis; this article by Doug Dillon and Allen Stenger.

Factor the expression A³(B-C) + B³(C-A) + C³(A-B).

Where does one even start??

Hint 1

Note that the expression is zero if B = C, or if A = C, or if A = B. This means that B - C, C - A, A - B must all be factors. If you factor these out, what is left over?

Need another hint? Click here.

Click here for the complete solution.