题目

如何因式分解：1：x^2+xy-2y^2-x+7y-6
2 :(x+y-2xy)(x+y-2)+(xy-1)^2
3 1999x^2-(1999^2-1)x-1999
4 x^2y-y^2z+z^2x-x^2z+y^2x+z^2y-2xyz

提问时间：2020-07-31

答案

3.1999x^2-(1999^2-1)x-1999=1999x(x-1999)+(x-1999)=(1999x+1)(x-1999)
4.x^2y-y^2z+z^2x-x^2z+y^2x+z^2y-2xyz
=(-y^2z-x^2z-2xyz)+(z^2x+z^2y)+(y^2x+x^2y)
=-z(x+y)^2+xy(x+y)+z^2(x+y)
=(x+y)((xy-yz)+(z^2-zx))
=(x+y)(x-z)(y-z)