6x^2-7xy-3y^2-xz+7yz-2z^2

方法1
因为6x^2-7xy-3y^2=(3x+y)(2x-3y)
而-2z^2=-2z*z
利用十字相乘法得
3x+y -2z
2x-3y +z
6X^2-7xy-3y^2-xz+7yz-2z^2=(3x+y-2z)(2x-3y+z)
方法二:待定系数法:
6x^2-7xy-3y^2-xz+7yz-2z^2
=(a1x+b1y+c1z)(a2x+b2y+c2z)
=a1a2x²+b1b2y²+c1c2z²+(a1b2+a2b1)xy+(a1c2+a2c1)xz+(b1c2+b2c1)yz
对应项系数相等
a1a2=6
b1b2=-3
c1c2=-2
a1b2+a2b1=-7
a1c2+a2c1=-1
b1c2+b2c1=7
解得
a1=2
a2=3
b1=-3
b2=1
c1=1
c2=-2
所以
6x^2-7xy-3y^2-xz+7yz-2z^2
=(2x-3y+z)(3x+y-2z)