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Step-by-step explanation:
x^4+2x^3y -2xy^3-y4
=((x^2)^2-(y^2)^2) + 2xy(x^2-y^2)
=(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)^3(x-y)
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