Question

4．现规定：|$\begin{array}{l}a&b\\ c&d\end{array}$|=a-b+c-d，则|$\begin{array}{l}{xy-3{x^2}}&{-2xy-{x^2}}\\{-2{x^2}-3}&{-5+xy}\end{array}$|=2xy-4x²+2．

Answer 1

分析 首先根据例题可得|$\begin{array}{l}{xy-3{x^2}}&{-2xy-{x^2}}\\{-2{x^2}-3}&{-5+xy}\end{array}$|=（xy-3x²）-（-2xy-x²）+（-2x²-3）-（-5+xy），然后再去括号，合并同类项即可．

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．
故答案为：2xy-4x²+2．

点评 此题主要考查了整式的加减，关键是弄懂例题含义，列出式子．