Question

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

Answer 1

分析 根據(jù)非負(fù)數(shù)的性質(zhì)，可求出x、y的值，然后將代數(shù)式化簡(jiǎn)再代值計(jì)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，
當(dāng)$\left\{\begin{array}{l}{x=-2}\\{y=4}\end{array}\right.$時(shí)，原式=3×（-2）×4-4×（-2）²=-24-16=-40．

點(diǎn)評(píng) 本題考查了整式的化簡(jiǎn)求值，利用非負(fù)數(shù)的和為零得出x、y的值是解題關(guān)鍵．