21081中２・式の計算・計算問題・多項式と数の除法1

$\begin{eqnarray}(1)\quad\;\;(\,8x-12y\,)\div 4\end{eqnarray}\;\;$

$\begin{eqnarray}\quad\;\;&=&(\,8x-12y\,) \times \dfrac{1}{\,4\,}\\[6pt]&=&8x\times \dfrac{1}{\,4\,}-12y \times \dfrac{1}{\,4\,}\\[6pt]&=&2x-3y\end{eqnarray}\;\;$

答$2x-3y$

$\begin{eqnarray}(2)\quad\;\;(\,-12a^{2}+18a\,)\div (\,-3\,)\end{eqnarray}\;\;$

$\begin{eqnarray}\quad\;\;&=&(\,-12a^{2}+18a\,)\times \Bigl(\,-\dfrac{1}{\;3\;}\,\Bigr)\\[6pt]&=&-12a^{2}\times \Bigl(\,-\dfrac{1}{\;3\;}\,\Bigr)+18a \times \Bigl(\,-\dfrac{1}{\;3\;}\,\Bigr)\\[6pt]&=&4a^{2}-6a\end{eqnarray}\;\;$

答$4a^{2}-6a$

$\begin{eqnarray}(3)\quad\;\;(\,24a+30b-6\,)\div 6\end{eqnarray}\;\;$

$\begin{eqnarray}\quad\;\;&=&(\,24a+30b-6\,)\times \Bigl(\,\dfrac{1}{\,6\,}\,\Bigr)\\[6pt]&=&24a\times \Bigl(\,\dfrac{1}{\,6\,}\,\Bigr)+30b\times \Bigl(\,\dfrac{1}{\,6\,}\,\Bigr)-6 \times \Bigl(\,\dfrac{1}{\,6\,}\,\Bigr)\\[6pt]&=&4a+5b-1\end{eqnarray}\;\;$

答$4a+5b-1$

$\begin{eqnarray}(4)\quad\;\;(\,-81x^{2}-36x-63\,)\div (\,-9\,)\end{eqnarray}\;\;$

$\begin{eqnarray}\quad\;\;&=&(\,-81x^{2}-36x-63\,)\times \Bigl(\,-\dfrac{1}{\,9\,}\,\Bigr)\\[6pt]&=&-81x^{2}\times \Bigl(\,-\dfrac{1}{\,9\,}\,\Bigr)-36x\times \Bigl(\,-\dfrac{1}{\,9\,}\,\Bigr)-63 \times \Bigl(\,-\dfrac{1}{\,9\,}\,\Bigr)\\[6pt]&=&9x^{2}+4x+7\end{eqnarray}\;\;$

答$9x^{2}+4x+7$

$\begin{eqnarray}(5)\quad\;\;(\,-30a^{2}-60ab+45b^{2}\,)\div (\,-15\,)\end{eqnarray}\;\;$

$\begin{eqnarray}\quad\;\;&=&(\,-30a^{2}-60ab+45b^{2}\,)\times \Bigl(\,-\dfrac{1}{\,15\,}\,\Bigr)\\[6pt]&=&-30a^{2}\times \Bigl(\,-\dfrac{1}{\,15\,}\,\Bigr)-60ab\times \Bigl(\,-\dfrac{1}{\,15\,}\,\Bigr)+45b^{2} \times \Bigl(\,-\dfrac{1}{\,15\,}\,\Bigr)\\[6pt]&=&2a^{2}+4ab-3b^{2}\end{eqnarray}\;\;$

答$2a^{2}+4ab-3b^{2}$