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(x-2)³-(y-2)³-(x-y)³ 9x²-6x-y²+4y-3

解答:

1.(x-2)^3-(y-2)^3-(x-y)^3
=(x-2)^3-(y-2)^3-((x-2)-(y-2))^3
=(x-2)^3-(y-2)^3-((x-2)^3-3(x-2)^2(y-2)+3(x-2)(y-2)^2-(y-2)^3)
=3(x-2)^2(y-2)-3(x-2)(y-2)^2
=3(x-2)(y-2)(x-y)
2.9x²-6x-y²+4y-3
=(9x²-6x+1)-(y²-4y+4)
=(3x-1)²-(x-2)²