高一因式分解题

来源：百度知道 编辑：UC知道 时间：2024/04/29 06:18:44
xyz-xy-xz+x-yz+y+z-1
详细过程

xyz-xy-xz+x-yz+y+z-1
=xy(z-1)-x(z-1)-y(z-1)+(z-1)
=(z-1)(xy-x-y+1)
=(z-1)[x(y-1)-(y-1)]
=(z-1)(y-1)(x-1)

两两结合：
=xy(z-1)-x(z-1)-y(z-1)+(z-1)
=(z-1)(xy-x-y+1)
=(z-1)[x(y-1)-(y-1)]
=(z-1)(y-1)(x-1)

xyz-xy-xz+x-yz+y+z-1

提取公因子Z-1，得：

=（z-1）*[xy-x-y+1]

提取公因子Y-1，得：

=（z-1）*(y-1)*(x-1)

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

xyz-xy-xz+x-yz+y+z-1
=xy(z-1)-x(z-1)-y(z-1)+(z-1)
=xy(z-1)-x(z-1)-(y-1)(z-1)
=[xy-x-(y-1)](z-1)
=[x(y-1)(y-1)](z-1)
=(x-1)(y-1)(z-1)
关键是看出公因子是(z-1)
解题表想什么捷径,数学多做题,时间长了就有感觉了.

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