Question

(X－2)的三次方减（y－2)的三次方减（x－y)的三次方是多少？要快哦

Answer 1

(x-2)³-(y-2)³-(x-y)³
=x³-6x²+12x-8-y³+6y²-12y+8-x³+3x²y-3xy²+y³
=-6x²+12x+6y²-12y+3x²y-3xy²

追问

抱歉，能分解因式么

追答

也是很烦的

(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)(x²-4x+4+xy-2x-2y+4+y²-4y+4-x²+2xy-y²）
=(x-y)(3xy-6x-6y+12)
=3(x-y)(xy-2x-2y+4)
=3(x-y)(x-2)(y-x)

其中：xy-2x-2y+4=(xy-2x)-(2y-4)=x(y-2)-2(y-2)=(y-2)(x-2)