Question

(x-2)^3-(y-2)^3-(x-y)^3

分解因式；x+y+xy+1等于多少?为什么？

Answer 1

1.=[(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)
2.=y(x+1)+(x+1)
=(y+1)(x+1)

Answer 2

(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)

Answer 3

（x+1）（y+1）