已知x+y=7,xy=2,则x³y-2x²y²+xy³等于?

已知x+y=7,xy=2,则x³y-2x²y²+xy³等于?
已知x+y=7,xy=2,则x³y-2x²y²+xy³等于?

已知x+y=7,xy=2,则x³y-2x²y²+xy³等于?
x³y-2x²y²+xy³
=xy(x²-2xy+y²)
=xy(x-y)²
=2×7²
=98

x+y=7, xy=2
x²+y²+2xy=49
(x-y)²=49-4xy
∴x³y-2x²y²+xy³
=xy(x²-2xy+y²)
=xy(x-y)²
=xy(49-4xy)
=2×(49-4×2)
=86