21021中２・式の計算・計算問題・多項式の加法1

$\begin{eqnarray}(1)\quad\;\;(\,x+3\,)+(\,x-2\,)\end{eqnarray}\;\;$

$\begin{eqnarray}\quad\;\;&=&x+3+x-2\\[5pt]&=&x+x+3-2\\[5pt]&=&2x+1\end{eqnarray}\;\;$

答$2x+1$

$\begin{eqnarray}(2)\quad\;\;(\,3a+b\,)+(\,4a+6b\,)\end{eqnarray}\;\;$

$\begin{eqnarray}\quad\;\;&=&3a+b+4a+6b\\[5pt]&=&3a+4a+b+6b\\[5pt]&=&7a+7b\end{eqnarray}\;\;$

答$7a+7b$

$\begin{eqnarray}(3)\quad\;\;(\,-4x^{2}-3xy\,)+(\,-7x^{2}+2xy\,)\end{eqnarray}\;\;$

$\begin{eqnarray}\quad\;\;&=&-4x^{2}-3xy-7x^{2}+2xy\\[5pt]&=&-4x^{2}-7x^{2}-3xy+2xy\\[5pt]&=&-11x^{2}-xy\end{eqnarray}\;\;$

答$-11x^{2}-xy$

$\begin{eqnarray}(4)\quad\;\;(\,-2x-5y+9\,)+(\,x-7y-4\,)\end{eqnarray}\;\;$

$\begin{eqnarray}\quad\;\;&=&-2x-5y+9+x-7y-4\\[5pt]&=&-2x+x-5y-7y+9-4\\[5pt]&=&-x-12y+5\end{eqnarray}\;\;$

答$-x-12y+5$

$\begin{eqnarray}(5)\quad\;\;(\,6a^{2}-4a-5\,)+(\,-5a^{2}-9a+7\,)\end{eqnarray}\;\;$

$\begin{eqnarray}\quad\;\;&=&6a^{2}-4a-5-5a^{2}-9a+7\\[5pt]&=&6a^{2}-5a^{2}-4a-9a-5+7\\[5pt]&=&a^{2}-13a+2\end{eqnarray}\;\;$

答$a^{2}-13a+2$

$\begin{eqnarray}(6)\quad\;\;(\,2x^{2}+8xy-3y^{2}\,)+(\,6x^{2}-7xy-y^{2}\,)\end{eqnarray}\;\;$

$\begin{eqnarray}\quad\;\;&=&2x^{2}+8xy-3y^{2}+6x^{2}-7xy-y^{2}\\[5pt]&=&2x^{2}+6x^{2}+8xy-7xy-3y^{2}-y^{2}\\[5pt]&=&8x^{2}+xy-4y^{2}\end{eqnarray}\;\;$

答$8x^{2}+xy-4y^{2}$