Factoring equation with 4 cubed numbers

Question

The problem is to factor $a^3x - b^3y + b^3x - a^3y$, and the answer is $$(x-y)(a+b)(a^2 - ab + b^2).$$

I got as far as $(x-y)(a^3 - b^3 + b^3 - a^3)$. I mean the above answer fits if it was just $a^3 + b^3$ but with that…

Answer 1

\begin{align*} a^3x-b^3y+b^3x-a^3y &= (a^3x+b^3x)-(a^3y+b^3y) \\ &= x(a^3+b^3)-y(a^3+b^3) \\ &= (x-y)(a^3+b^3) \\ &= (x-y)(a+b)(a^2-ab+b^2) \end{align*}

Answer 2

Your first step should have been $a^3x-b^3y+b^3x-a^3y = (x-y)(a^3+b^3)$.

Then, use the factorization $a^3+b^3 = (a+b)(a^2-ab+b^2)$.