因式分解一题,(x-2)^3-(y-2)^3-(x-y)^3

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因式分解一题,(x-2)^3-(y-2)^3-(x-y)^3
因式分解一题,
(x-2)^3-(y-2)^3-(x-y)^3

因式分解一题,(x-2)^3-(y-2)^3-(x-y)^3
(x-2)^3-(y-2)^3-(x-y)^3
=[(x-2)-(y-2)][(x-2)^2+(x-2)(y-2)+(y-2)^2]-(x-y)^3
=(x-y)[(x-2)^2+(x-2)(y-2)+(y-2)^2-(x-y)^2]
=(x-y)(3xy-6x-6y+12) (中括号内展开,合并同类项可得)
=(x-y)[3x(y-2)-6(y-2)]
=(x-y)(y-2)(3x-6)
=3(x-y)(y-2)(x-2)