因式分解之类的三道数学题.

题目

因式分解之类的三道数学题.
-ab（2a-b）²+b（b-2a）²
-9m（m-n）-6m（n-m）²
81（x-y）²-16（x+y）²

答案

解
-ab(2a-b)²+b(b-2a)²
=-ab(2a-b)²+b(2a-b)²
=(2a-b)(b-ab)
=b(2a-b)(1-a)
-9m(m-n)-6m(n-m)²
=9m(n-m)-6m(n-m)²
=3m(n-m)[3-2(n-m)]
=3m(n-m)(3-2n+2m)
81(x-y)²-16(x+y)²
=[9(x-y)+4(x+y)][9(x-y)-4(x+y)]
=(9x-9y+4x+4y)(9x-9y-4x-4y)
=(13x-5y)(5x-13y)