How to factor intricate polynomial $ ab^3 - a^3b + a^3c -ac^3 +bc^3 - b^3c $ I would like to know how to factor the following polynomial. 
$$ ab^3 - a^3b + a^3c -ac^3 +bc^3 - b^3c $$
What is the method I should use to factor it? If anyone could help.. Thanks in advance.

\begin{align*}
ab^3 - a^3b + a^3c -ac^3 +bc^3 - b^3c&=-a^3(b-c)+b^3(a-c)+c^3(b-a)\\
&=-a^3(b-c)+b^3(a-c)+c^3[(b-c)+(c-a)]\\
&=(c^3-a^3)(b-c)+(b^3-c^3)(a-c)\\
&=(c-a)(c^2+ac+a^2)(b-c)+(b-c)(b^2+bc+c^2)(a-c)\\
&=(a-c)(b-c)(-c^2-ac-a^2+b^2+bc+c^2)\\
&=(a-c)(b-c)(b^2+bc-ac-a^2)\\
&=(a-c)(b-c)[(b+a)(b-a)+c(b-a)]\\
&=(a-c)(b-c)(b-a)(a+b+c)\\
&=(a-b)(b-c)(c-a)(a+b+c)\\
\end{align*}
