已知m-n=4,mn=-3,求m^3n+mn^3+2m^2n^2的值
问题描述：
已知m-n=4,mn=-3,求m^3n+mn^3+2m^2n^2的值
答
m^3n+mn^3+2m^2n^2
=mn(m+n)^2
=-48.
答
m^3*n+mn^3+2m^2n^2
=mn(m^2+n^2+2mn)
=mn(m+n)^2
=-3*4^2
=-48
应该是+2m^2n^2的加号错误
或m-n=4的减号错误
答
首先：m^3n+mn^3+2m^2n^2
=mn(n^2+m^2+2mn)
=mn(n+m)^2
接着因为
(m+n)^2=(m-n)^2-4mn
代入数值有
(16-12)*(-3)=-12
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