# How do you factor x^(3a) y^a - y^(3a) x^a?

Decompose the terms of ${x}^{3 a} {y}^{a} - {y}^{3 a} {x}^{a}$
$= {x}^{2 a} \cdot {x}^{a} \cdot {y}^{a} - {x}^{a} \cdot {y}^{a} \cdot {y}^{2 a}$
$\textcolor{w h i t e}{\text{XXXX}}$now we can see an obvious common term x^ay^a =(x^ay^a)(x^(2a)-y^(2a))
$= \left({x}^{a} {y}^{a}\right) \left({\left({x}^{a}\right)}^{2} - {\left({y}^{a}\right)}^{2}\right)$
$\textcolor{w h i t e}{\text{XXXX}}$the second term is the difference of squares, so
=(x^ay^a)((x^a+y^a)(x^a-y^a)#