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=

Question

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=

Answer 1

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