已知x-y=-1,xy=3,求x^3y-2x^2y^2+xy^3的值

已知x-y=-1,xy=3,求x^3y-2x^2y^2+xy^3的值
已知x-y=-1,xy=3,求x^3y-2x^2y^2+xy^3的值

已知x-y=-1,xy=3,求x^3y-2x^2y^2+xy^3的值
x³y-2x²y²+xy³
=xy(x²-2xy+y²)
=xy(x-y)²
=3(-1)²
=3

因为x-y=-1，xy=3
所以x^3y-2x^2y^2+xy^3
=x^2(xy)-2(xy)xy+(xy)y^2
=3x^2-2(3)xy+3y^2
=3(x-y)^2
=3(-1)^2
=3

x³y-2x²y²+xy³
=xy(x²-2xy+y²)
=xy(x-y)²
=3(-1)²
=3