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