计算（m-n)^3+(n-m)m^2

题目

计算（m-n)^3+(n-m)m^2
^3代表立方

答案

（m-n)^3+(n-m)m^2
=（m-n)^3-(m-n)m^2
=(m-n)[(m-n)^2-m^2]
=(m-n)(m-n+m)(m-n-m)
=-n(m-n)(2m-n)
=-n(2m^2-3mn+n^2)
=-2m^2n+3mn^2-n^3