Factorise (x^2+xy) ^2 - (xy+y^2) ^2

We are given with

(x² + xy) ² - (xy + y²) ²

which is a difference of two square with factors of:

[ (x² + xy) + (xy + y²) ][ (x² + xy) - (xy + y²) ]

Simplifying:

(x² + xy + xy + y²) (x² + xy - xy - y²)

(x² + 2xy + y²) (x² - y²)

Which can be further factored into:

(x + y) ² (x + y) (x - y)

or in simplest form:

(x + y) ³ (x - y)