有这样一道题,计算：（x-y)[(x+y)(x+y)-xy]-(x-y)[(x-y)(x-y)+xy]的值,其中x=2006,y=2007；某同学把“Y=

题目

有这样一道题,计算：（x-y)[(x+y)(x+y)-xy]-(x-y)[(x-y)(x-y)+xy]的值,其中x=2006,y=2007；某同学把“Y=

答案

原式=(x-y)(x²+2xy+y²-xy)-(x-y)(x²-2xy+y²+xy)=(x-y)(x²+xy+y²)-(x+y)(x²-xy+y²)=(x³-y³)-(x³+y³)=-2y³结果和x无关所以不蹲x取何值,结果都不变...