Question

4．現(xiàn)規(guī)定：|$\begin{array}{l}a&b\\ c&d\end{array}$|=a-b+c-d，則|$\begin{array}{l}{xy-3{x^2}}&{-2xy-{x^2}}\\{-2{x^2}-3}&{-5+xy}\end{array}$|=2xy-4x²+2．

Answer 1

分析 首先根據(jù)例題可得|$\begin{array}{l}{xy-3{x^2}}&{-2xy-{x^2}}\\{-2{x^2}-3}&{-5+xy}\end{array}$|=（xy-3x²）-（-2xy-x²）+（-2x²-3）-（-5+xy），然后再去括號(hào)，合并同類項(xiàng)即可．

解答 解：∵|$\begin{array}{l}a&b\\ c&d\end{array}$|=a-b+c-d，
∴|$\begin{array}{l}{xy-3{x^2}}&{-2xy-{x^2}}\\{-2{x^2}-3}&{-5+xy}\end{array}$|
=（xy-3x²）-（-2xy-x²）+（-2x²-3）-（-5+xy）
=xy-3x²+2xy+x²-2x²-3+5-xy
=2xy-4x²+2．
故答案為：2xy-4x²+2．

點(diǎn)評(píng) 此題主要考查了整式的加減，關(guān)鍵是弄懂例題含義，列出式子．