-9(x+y)²+(x-y)² 因式分解

题目

-9(x+y)²+(x-y)² 因式分解

答案

-9(x+y)²+(x-y)²
=(x-y)² -[3(x+y)]²
=[(x-y)-3(x+y)][(x-y)+3(x+y)]
=(x-y-3x-3y)(x-y+3x+3y)
=-（2x+4y）(4x+2y)
=-4(x+2y)(2x+y)