首页 > 留学知识库

问题: (x-2)三次方-(Y-2)三次方-(X-Y)三次方

解答:


(x-2)^3-(y-2)^3-(x-y)^3
=(x-2)^3-(y-2)^3-[(x-2)-(y-2)]^3
=(x-2)^3-(y-2)^3-[(x-2)^3-3(x-2)^2(y-2)+3(x-2)(y-2)^2-(y-2)^3]
=3(x-2)^2(y-2)-3(x-2)(y-2)^2
=3(x-2)(y-2)[(x-2)-(y-2)]
=3(x-2)(y-2)(x-y)