x^4 - 2(x^3)(y) - y^4 + 2xy^3

= (x^4 - y^4) + ( -2(x^3)y + 2x(y^3) )

= (x^2 - y^2)(x^2 - y^2) - 2xy(x^2 - y^2)

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

= (x + y) (x - y) (x - y)^2

= (x + y) (x - y)^3

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