2(x+y)(x+y-z)+3(y-z)(x+y-z)

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/05 17:29:31

2(x+y)(x+y-z)+3(y-z)(x+y-z)
2(x+y)(x+y-z)+3(y-z)(x+y-z)

2(x+y)(x+y-z)+3(y-z)(x+y-z)
(x+y-z)(2x+5y-3z)
是不是这个答案

因为原式为x,y,z的5次轮换式当x=y时原式为0
(x-y)(y-z)(z-x)为因式设:(y-z)^5+(z-x)^5+(x-y)^5=(x-y)(y-z)(z-x)[l(x^2+y^2+z^2)+m(xy+yz+xz)]
令x=1 y=2 z=0 5l+2m=15
令x=1 z=-1 y=0 2l-m=15
l=5 m=-5
(y-z)^5+(z-x)...

全部展开

因为原式为x,y,z的5次轮换式当x=y时原式为0
(x-y)(y-z)(z-x)为因式设:(y-z)^5+(z-x)^5+(x-y)^5=(x-y)(y-z)(z-x)[l(x^2+y^2+z^2)+m(xy+yz+xz)]
令x=1 y=2 z=0 5l+2m=15
令x=1 z=-1 y=0 2l-m=15
l=5 m=-5
(y-z)^5+(z-x)^5+(x-y)^5=5(x-y)(y-z)(z-x)[x^2+y^2+z^2-xy-yz-xz]

收起