x^-xy-2y^=0怎么化简成(x-2y)(x+y)=0

题目

x^-xy-2y^=0怎么化简成(x-2y)(x+y)=0

答案

∵x²-xy-2y²
=x²-xy-y²-y²
=(x²-y²)-(xy+y²)
=(x+y)(x-y)-y(x+y)
=(x+y)(x-y-y)
=(x+y)(x-2y)
∴x²-xy-2y²=0可化为(x-2y)(x+y)=0