已知X+Y=7,XY=12,求X的三次方乘以Y减2X平方Y平方加XY的三次方的值.

题目

已知X+Y=7,XY=12,求X的三次方乘以Y减2X平方Y平方加XY的三次方的值.

答案

x^3y-2x^2y^2+xy^3
=x^3y+2x^2y^2+xy^3-4x^2y^2
=xy(x^2+2xy+y^2)-4x^2y^2
=xy(x+y)^2-4x^2y^2
=12×7×7-4×12×12
=588-576
=12