好吧问答库 > 数学因式分解：x눀-x눀y+xy눀-x+y-y눀,我要详细过程，让我看得懂

数学因式分解：x눀-x눀y+xy눀-x+y-y눀,我要详细过程，让我看得懂

2024年11月18日 07:34

有4个网友回答

网友（1）：

原式=x²(1-y)+x(y²-1)+y(1-y)
=x²(1-y)-x(1+y)(1-y)+y(1-y)
=(1-y)(x²-x-xy+y)
=-(y-1)[x(x-1)-y(x-1)]
=-(y-1)(x-1)(x-y)

网友（2）：

x²-x²y+xy²-x+y-y²
=(x²-y²)-(x²y-xy²)-(x-y)
=(x-y)(x+y)-xy(x-y)-(x-y)
=(x-y)(x+y-xy-1)
=-(x-y)(xy-x-y+1)
=-(x-y)[(xy-x)-(y-1)]
=-(x-y)[x(y-1)-(y-1)]
=-(x-y)(x-1)(y-1)

网友（3）：

x²-y²+xy²-x²y-(x-y)=(x-y)(x+y)-xy(x-y)-(x-y)=(x-y)(x+y-xy-1)=-(x-y)(x(y-1)-(y-1))=-(x-y)(x-1)(y-1)

网友（4）：

x²-x²y+xy²-x+y-y²
=x²-y²-(x²y-xy²)-(x-y)
=(x+y)(x-y)-xy(x-y)-(x-y)
=(x-y)(x+y-xy-1)
=(x-y)[(x-xy)+(y-1)]
=(x-y)[x(1-y)-(1-y)]
=(x-y)(1-y)(x-1)