已知x-y=1,xy=3,求x³y-2x²y²+xy³的值

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已知x-y=1,xy=3,求x³y-2x²y²+xy³的值
已知x-y=1,xy=3,求x³y-2x²y²+xy³的值

已知x-y=1,xy=3,求x³y-2x²y²+xy³的值
解
x³y-2x²y²+xy³
=xy(x²-2xy+y²)
=xy(x-y)²
=3×1²
=3

x-y=1,xy=3,
x³y-2x²y²+xy³
＝xy﹙x²－2xy＋y²﹚
＝xy﹙x－y﹚²
＝3×1²
＝3.