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(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)(x^2+xy+y^2) =(x-y)(x^2-4x+4+xy-2x-2y+4+y^2-4y+4)-(x-y)(x^2+xy+y^2) =(x-y)(x^2-4x+4+xy-2x-2y+4+y^2-4y+4-x^2-xy-y^2) =(x-y)(-6x-6y+12) =-6(x-y)(x+y-2) x+y+xy+1 =(x+xy)+(y+1) =x(1+y)+(y+1) =(y+1)(x+1)
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