21072中２・式の計算・計算問題・多項式と数の乗法2

分 配 法 則

１．①，②の順にかけ合わせます

２．①，②，③の順にかけ合わせます

$\begin{eqnarray}(1)\quad\;\;-5(\,0.8x-1.2y\,)\end{eqnarray}\;\;$

$\begin{eqnarray}\quad\;\;&=&\color{red}-5\times \color{black}0.8x\color{red}-5\times \color{black}(\,-1.2y\,)\\[5pt]&=&-4x+6y\end{eqnarray}\;\;$

答$-4x+6y$

$\begin{eqnarray}(2)\quad\;\;\dfrac{1}{\;3\;}(\,-12a+15b\,)\end{eqnarray}\;\;$

$\begin{eqnarray}\quad\;\;&=&\color{red}\dfrac{1}{\;3\;}\times\color{black} (\,-12a\,)\color{red}+\dfrac{1}{\;3\;}\times\color{black}15b\\[6pt]&=&-4a+5b\end{eqnarray}\;\;$

答$-4a+5b$

$\begin{eqnarray}(3)\quad\;\;18\Bigl(\,\dfrac{\;1\;}{\;6\;}x-\dfrac{2}{\;3\;}y-0.5\,\Bigr)\end{eqnarray}\;\;$

$\begin{eqnarray}\quad\;\;&=&\color{red}18\times\color{black}\dfrac{\;1\;}{\;6\;}x\color{red}+18\times\color{black}\Bigl(\,-\dfrac{2}{\;3\;}y\,\Bigr) \color{red}+18\times\color{black} \Bigl(\,-\dfrac{1}{\;2\;}\,\Bigr)\\[6pt]&=&3x-12y-9\end{eqnarray}\;\;$

答$3x-12y-9$

$\begin{eqnarray}(4)\quad\;\;(\,24a^{2}+48a-16\,)\times\Bigl(\,-\dfrac{1}{\;8\;}\,\Bigr)\end{eqnarray}\;\;$

$\begin{eqnarray}\quad\;\;&=&24a^{2}\color{red}\times\Bigl(\,-\dfrac{1}{\;8\;}\,\Bigr)\color{black}+48a\color{red}\times\Bigl(\,-\dfrac{1}{\;8\;}\,\Bigr)\color{black}-16\color{red}\times\Bigl(\,-\dfrac{1}{\;8\;}\,\Bigr)\\[6pt]&=&-3a^{2}-6a+2\end{eqnarray}\;\;$

答$-3a^{2}-6a+2$

$\begin{eqnarray}(5)\quad\;\;\Bigl(\,-\dfrac{\;2\;}{\;3\;}x^{2}+\dfrac{8}{\;15\;}xy-\dfrac{\;5\;}{6}y^{2}\,\Bigr)\times 30\end{eqnarray}\;\;$

$\begin{eqnarray}\quad\;\;&=&-\dfrac{2}{\;3\;}x^{2}\color{red}\times 30\color{black} +\dfrac{8}{\;15\;}xy\color{red}\times 30\color{black}-\dfrac{5}{\;6\;}y^{2}\color{red}\times 30\\[6pt]&=&-20x^{2}+16xy-25y^{2}\end{eqnarray}\;\;$

答$-20x^{2}+16xy-25y^{2}$

$\begin{eqnarray}(6)\quad\;\;\Bigl(\,1.6a^{2}+4.8ab-7.2b^{2}\,\Bigr)\times\Bigl(\,-\dfrac{5}{\;2\;}\,\Bigr)\end{eqnarray}\;\;$

$\begin{eqnarray}\quad\;\;&=&\dfrac{8}{\;5\;}a^{2}\color{red}\times\Bigl(\,-\dfrac{5}{\;2\;}\,\Bigr)\color{black}+\dfrac{\;24\;}{\;5\;}ab\color{red}\times\Bigl(\,-\dfrac{5}{\;2\;}\,\Bigr)\color{black}-\dfrac{\;36\;}{\;5\;}b^{2}\color{red}\times\Bigl(\,-\dfrac{5}{\;2\;}\,\Bigr)\\[6pt]&=&-4a^{2}-12ab+18b^{2}\end{eqnarray}\;\;$

答$-4a^{2}-12ab+18b^{2}$