因式分解(x-2)³-(y-2)³-(x-y)³
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(x-2)³-(y-2)³-(x-y)³
=(x-y)(x²-4x+4+xy-2x-2y+4+y²-4y+4)-(x-y)³
=(x-y)(x²+y²-6x-6y+12+xy-x²+2xy-y²)
=(x-y)(3xy-6x-6y+12)
=3(x-y)(xy-2x-2y+4)
=3(x-y)(x-2)(y-2)
=(x-y)(x²-4x+4+xy-2x-2y+4+y²-4y+4)-(x-y)³
=(x-y)(x²+y²-6x-6y+12+xy-x²+2xy-y²)
=(x-y)(3xy-6x-6y+12)
=3(x-y)(xy-2x-2y+4)
=3(x-y)(x-2)(y-2)
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