Question

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

Answer 1

Decompose the terms of `x^(3a)y^a - y^(3a)x^a`
as
`= x^(2a)*x^a*y^a - x^a*y^a*y^(2a)`
`color(white)("XXXX")`now we can see an obvious common term `x^ay^a`=(x^ay^a)(x^(2a)-y^(2a))#

`=(x^ay^a)((x^a)^2 -(y^a)^2)`
`color(white)("XXXX")`the second term is the difference of squares, so
`=(x^ay^a)((x^a+y^a)(x^a-y^a)`