(x-y)^2(x+y)^2-2(y-x)^3-(y-x)^4,分解因式,
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(x-y)^2(x+y)^2-2(y-x)^3-(y-x)^4
=(x-y)^2(x+y)^2+2(x-y)^3+(x-y)^4
=(x-y)^2[(x+y)^2+2(x-y)+(x-y)^2]
=(x-y)^2(x^2+2xy+y^2-2x-2y+x^2-2xy+y^2)
=(x-y)^2(2x^2+2y^2-2x-2y)
=2(x-y)^2(x^2+y^2-x-y)
=(x-y)^2(x+y)^2+2(x-y)^3+(x-y)^4
=(x-y)^2[(x+y)^2+2(x-y)+(x-y)^2]
=(x-y)^2(x^2+2xy+y^2-2x-2y+x^2-2xy+y^2)
=(x-y)^2(2x^2+2y^2-2x-2y)
=2(x-y)^2(x^2+y^2-x-y)
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