21031中２・式の計算・計算問題・多項式の減法1

$\begin{eqnarray}(1)\quad\;\;(\,x+5\,)-(\,x+4\,)\end{eqnarray}\;\;$

$\begin{eqnarray}\quad\;\;&=&x+5\color{red}-\color{black}x\color{red}-\color{black}4\\[5pt]&=&x-x+5-4\\[5pt]&=&1\end{eqnarray}\;\;$

答$1$

$\begin{eqnarray}(2)\quad\;\;(\,6a-b\,)-(\,5a-2b\,)\end{eqnarray}\;\;$

$\begin{eqnarray}\quad\;\;&=&6a-b\color{red}-\color{black}5a\color{red}+\color{black}2b\\[5pt]&=&6a-5a-b+2b\\[5pt]&=&a+b\end{eqnarray}\;\;$

答$a+b$

$\begin{eqnarray}(3)\quad\;\;(\,3x^{2}+7xy\,)-(\,-12x^{2}+8xy\,)\end{eqnarray}\;\;$

$\begin{eqnarray}\quad\;\;&=&3x^{2}+7xy\color{red}+\color{black}12x^{2}\color{red}-\color{black}8xy\\[5pt]&=&3x^{2}+12x^{2}+7xy-8xy\\[5pt]&=&15x^{2}-xy\end{eqnarray}\;\;$

答$15x^{2}-xy$

$\begin{eqnarray}(4)\quad\;\;(\,-9x-2y-1\,)-(\,9x-y+1\,)\end{eqnarray}\;\;$

$\begin{eqnarray}\quad\;\;&=&-9x-2y-1\color{red}-\color{black}9x\color{red}+\color{black}y\color{red}-\color{black}1\,)\\[5pt]&=&-9x-9x-2y+y-1-1\\[5pt]&=&-18x-y-2\end{eqnarray}\;\;$

答$-18x-y-2$

$\begin{eqnarray}(5)\quad\;\;(\,8a^{2}+6a-9\,)-(\,-14a^{2}+5a-20\,)\end{eqnarray}\;\;$

$\begin{eqnarray}\quad\;\;&=&8a^{2}+6a-9\color{red}+\color{black}14a^{2}\color{red}-\color{black}5a\color{red}+\color{black}20\\[5pt]&=&8a^{2}+14a^{2}+6a-5a-9+20\\[5pt]&=&22a^{2}+a+11\end{eqnarray}\;\;$

答$22a^{2}+a+11$

$\begin{eqnarray}(6)\quad\;\;(\,15x^{2}-3xy+2y^{2}\,)-(\,25x^{2}-18xy-11y^{2}\,)\end{eqnarray}\;\;$

$\begin{eqnarray}\quad\;\;&=&15x^{2}-3xy+2y^{2}\color{red}-\color{black}25x^{2}\color{red}+\color{black}18xy\color{red}+\color{black}11y^{2}\\[5pt]&=&15x^{2}-25x^{2}-3xy+18xy+2y^{2}+11y^{2}\\[5pt]&=&-10x^{2}+15xy+13y^{2}\end{eqnarray}\;\;$

答$-10x^{2}+15xy+13y^{2}$