(xy-1)^2+(x+y-z)(x+y-zxy)因式分解

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/28 22:37:22
(xy-1)^2+(x+y-z)(x+y-zxy)因式分解

(xy-1)^2+(x+y-z)(x+y-zxy)因式分解
(xy-1)^2+(x+y-z)(x+y-zxy)因式分解

(xy-1)^2+(x+y-z)(x+y-zxy)因式分解
(xy-1)^2+(x+y-z)(x+y-zxy)
=(x^2y^2-2xy+1)+(x+y)^2-z(x+y)-zxy(x+y)+xyz^2
=x^2y^2-2xy+1+x^2+2xy+y^2-z[(x+y)+xy(x+y)]+xyz^2
=(x^2y^2+x^2+y^2+1)-z(x+y+x^2y+xy^2)+xyz^2
=(x^2+1)(y^2+1)-z[x(y^2+1)+y(x^2+1)]+xyz^2
设x^2+1=a,y^2+1=b
则上式=ab-z(bx+ay)+xyz^2
=ab-bxz-ayz+xyz^2
=b(a-xz)-yz(a-xz)
=(b-yz)(a-xz)
=(y^2+1-yz)(x^2+1-xz)