Question

1.因式分解m^2-5m-mn+5n 2.因式分解x(x+z)-y(y+z) 3.因式分解x^2+2xy-3y^+2xz+14yz-8z^2

Answer 1

1、
m^2-5m-mn+5n
=m(m-5)-n(m-5)
=(m-n)(m-5)
2、
x(x+z)-y(y+z)
=x^2+xz-y^2-yz
=(x+y)(x-y)+z(x-y)
=(x+y+z)(x-y)
3、
可以用待定系数法,设
x^2+2xy-3y^2+2xz+14yz-8z^2
=(x+ay+bz)(x+cy+dz)
=x^2+(a+c)xy+acy^2+(b+d)xz+(ad+bc)yz+bdz^2
a+c=2
ac=-3
b+d=2
bd=-8
ad+bc=14
解得:
a=3 b=-2 c=-1 d=4
代入,得
x^2+2xy-3y^+2xz+14yz-8z^2
=(x+3y-2z)(x-y+4z)