Question

16．已知（x+2）²+|x+y-2|=0，求3x²y+{-2x²y-[-2xy+（x²y-4x²）]-xy}的值．

Answer 1

分析 根据非负数的性质，可求出x、y的值，然后将代数式化简再代值计算．

解答 解：由（x+2）²+|x+y-2|=0，得　
$\left\{\begin{array}{l}{x+2=0}\\{x+y-2=0}\end{array}\right.$，
解得$\left\{\begin{array}{l}{x=-2}\\{y=4}\end{array}\right.$．
3x²y+{-2x²y-[-2xy+（x²y-4x²）]-xy}=3x²y+{-2x²y-[-2xy+x²y-4x²]-xy}
=3x²y+{-2x²y+2xy-x²y+4x²-xy}
=3x²y-2x²y+2xy-x²y-4x²+xy
=3xy-4x²，
当$\left\{\begin{array}{l}{x=-2}\\{y=4}\end{array}\right.$时，原式=3×（-2）×4-4×（-2）²=-24-16=-40．

点评 本题考查了整式的化简求值，利用非负数的和为零得出x、y的值是解题关键．