因式分解一题,要求过程

(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)

=(x-2)*(x^2-4x+4)-(y-2)*(y^2-4y+4)-(x-y)*(x^2-2xy+y^2)
=x^3-4x^2+4x-2x^2+8x-8-y^3+4y^2-4y+2y^2-8y+8-x^3+2x^2y-xy^2+x^2y-2xy^2+y^3
=-6x^2+12x+6y^2-12y+3x^2y-3xy^2