我数学不好,初二的问题帮我解下!谢

来源:百度知道 编辑:UC知道 时间:2024/06/11 17:14:46
(x+y-xy-1)^2 为什么等于x-1)^2(y-1)^2 ?

(x+y-xy-1)²
=[(x-xy)-(1-y)]²
=[x(1-y)-(1-y)]²
=[(1-y)(x-1)]²
=(1-y)²(x-1)²
=(x-1)²(y-1)²

x+y-xy-1=(x-1)(y-1)

你把右式展开就是(xy-x-y+1)^2了,平方项里面可以随便变换正负号。

x+y-xy-1
=X-XY+Y-1
=X(1-Y)+(Y-1)
=-X(Y-1)+(Y-1)
=(Y-1)(1-X)
(1-X)方=(X-1)方
所以
(x+y-xy-1)^2 等于(x-1)^2(y-1)^2 ?