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

$\begin{array}{r}(1)-5(0.8x-1.2y)\end{array}$

$\begin{array}{rcl}& =& -5\times 0.8x-5\times (-1.2y)\\ & =& -4x+6y\end{array}$

答$-4x+6y$

$\begin{array}{r}(2){\displaystyle \frac{1}{3}}(-12a+15b)\end{array}$

$\begin{array}{rcl}& =& {\displaystyle \frac{1}{3}}\times (-12a)+{\displaystyle \frac{1}{3}}\times 15b\\ & =& -4a+5b\end{array}$

答$-4a+5b$

$\begin{array}{r}(3)18({\displaystyle \frac{1}{6}}x-{\displaystyle \frac{2}{3}}y-0.5)\end{array}$

$\begin{array}{rcl}& =& 18\times {\displaystyle \frac{1}{6}}x+18\times (-{\displaystyle \frac{2}{3}}y)+18\times (-{\displaystyle \frac{1}{2}})\\ & =& 3x-12y-9\end{array}$

答$3x-12y-9$

$\begin{array}{r}(4)(24a^2+48a-16)\times (-{\displaystyle \frac{1}{8}})\end{array}$

$\begin{array}{rcl}& =& 24a^2\times (-{\displaystyle \frac{1}{8}})+48a\times (-{\displaystyle \frac{1}{8}})-16\times (-{\displaystyle \frac{1}{8}})\\ & =& -3a^2-6a+2\end{array}$

答$-3a^2-6a+2$

$\begin{array}{r}(5)(-{\displaystyle \frac{2}{3}}{x}^2+{\displaystyle \frac{8}{15}}xy-{\displaystyle \frac{5}{6}}{y}^2)\times 30\end{array}$

$\begin{array}{rcl}& =& -{\displaystyle \frac{2}{3}}{x}^2\times 30+{\displaystyle \frac{8}{15}}xy\times 30-{\displaystyle \frac{5}{6}}{y}^2\times 30\\ & =& -20x^2+16xy-25y^2\end{array}$

答$-20x^2+16xy-25y^2$

$\begin{array}{r}(6)(1.6a^2+4.8ab-7.2b^2)\times (-{\displaystyle \frac{5}{2}})\end{array}$

$\begin{array}{rcl}& =& {\displaystyle \frac{8}{5}}{a}^2\times (-{\displaystyle \frac{5}{2}})+{\displaystyle \frac{24}{5}}ab\times (-{\displaystyle \frac{5}{2}})-{\displaystyle \frac{36}{5}}{b}^2\times (-{\displaystyle \frac{5}{2}})\\ & =& -4a^2-12ab+18b^2\end{array}$

答$-4a^2-12ab+18b^2$