已知x+y=5,x2+y2=13,求代数式x3y+2x2y2+xy3的值.

问题描述:

已知x+y=5,x2+y2=13,求代数式x3y+2x2y2+xy3的值.

x3y+2x2y2+xy3=xy(x2+2xy+y2)=xy(x+y)2
∵x+y=5,
∴(x+y)2=25,
x2+y2+2xy=25,
∵x2+y2=13,
∴xy=6,
∴xy(x+y)2=6×25=150.