Factorise : (b-c)(b^3 + c^3) + (c-a)(c^3 + a^3) + (a-b)(a^3 + b^3)
If we put in the expression, we get:
so is a factor.
Similarly and are also factors.
Since the expression is of degree in , the remaining factor is linear, and by symmetry is therefore for some constant .
Compare coefficients of, say, (taking the from the first factor, the from the second, the from the third and the from the fourth)
Or did I cheat a bit?