利用作差法,比较当Y＜0时,比较A=x³-(2x²y-y²-3y)与B=x³-2x²y+y²+2y的大小

题目

利用作差法,比较当Y＜0时,比较A=x³-(2x²y-y²-3y)与B=x³-2x²y+y²+2y的大小

答案

A-B=x³-(2x²y-y²-3y)-(x³-2x²y+y²+2y)
=x³-2x²y+y²+3y-x³+2x²y-y²-2y
=3y-2y
=y
因为Y＜0,所以A-B＜0,即A＜B.