a^3(b-c)+b^3(c-a)+c^3(a-b)
=(b-c)a^3+(c^3-b^3)a+bc(b^2-c^2)
=(b-c){a^3-(b^2+bc+c^2)a+bc(b+c)}
=(b-c)(a-c){a^2+ca-b(b+c)}
=(b-c)(a-c)(a-b)(a+b+c)