已知m+n=3,mn=2/3,求m^3n-m^2n^2+nm^3怎么写

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已知m+n=3,mn=2/3,求m^3n-m^2n^2+nm^3怎么写已知m+n=3,mn=2/3,求m^3n-m^2n^2+nm^3怎么写已知m+n=3,mn=2/3,求m^3n-m^2n^2+nm

已知m+n=3,mn=2/3,求m^3n-m^2n^2+nm^3怎么写
已知m+n=3,mn=2/3,求m^3n-m^2n^2+nm^3怎么写

已知m+n=3,mn=2/3,求m^3n-m^2n^2+nm^3怎么写
m+n=3
平方
m²+2mn+n²=9
m²+n²
=9-2mn
=9-4/3
=23/3
所以原式=mn(m²+n²)+(mn)²
=46/9+4/9
=50/9

m^3n+nm^3-m^2n^2=mn(m^2+n^2-mn)=mn[(m+n)^2-3mn]=2/3(3*3-3*2/3)=14/3

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