(x+y-z)(x-y+z)+(y-x+z)(y-x-z)分解因式

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/28 01:13:37
(x+y-z)(x-y+z)+(y-x+z)(y-x-z)分解因式(x+y-z)(x-y+z)+(y-x+z)(y-x-z)分解因式(x+y-z)(x-y+z)+(y-x+z)(y-x-z)分解因式(

(x+y-z)(x-y+z)+(y-x+z)(y-x-z)分解因式
(x+y-z)(x-y+z)+(y-x+z)(y-x-z)分解因式

(x+y-z)(x-y+z)+(y-x+z)(y-x-z)分解因式
(x+y-z)(x-y+z)+(y-x+z)(y-x-z)
= -(x+y-z)(-x+y-z)+(y-x+z)(y-x-z)
= -(x+y-z)(y-x-z)+(y-x+z)(y-x-z)
= (y-x-z)(y-x+z-x-y+z)
= 2(y-x-z)(Z-x)

=x^2-xy+xz+xy-y^2+yz-xz+yz-z^2 + y^2-xy-yz-xy+x^2+xz+yz-xz-z^2
=2x^2-2z^2 -2xy +2yz
=2(x-z)(x+z) -2y(x-z)
=2(x-z)(x-y+z)