a^3(c−b^2)+b^3(a−c^2)+c^3(b−a^2)+abc(abc−1)
=a^3c−a^3b^2+b^3(a−c^2)+bc^3−a^2c^3+a^2b^2c^2−abc
=(a^3c−a^2c^3)+b^3(a−c^2)−(a^3b^2−a^2b^2c^2)+(bc^3−abc)
=a^2c(a−c^2)+b^3(a−c^2)−a^2b^2(a−c^2)−bc(a−c^2)
=(a^2c+b^3−a^2b^2−bc)(a−c2)
=[c(a^2−b)−b^2(a^2−b)](a−c^2)=(a^2-b)(c-b^2)(a-c^2)