31022中３・多項式の展開・計算問題・展開の公式1-2

(1) $\quad\;\,\begin{eqnarray}(\,2x+3\,)(\,2x+5\,)\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&(\,2x\,)^{2}+(\,3+5\,) \times 2x+(\,3\times 5\,)\\[6pt]&=&4x^{2}+16x+15\end{eqnarray}\;\;$

答$4x^{2}+16x+15$

(2) $\quad\;\,\begin{eqnarray}(\,3x-5\,)(\,3x-4\,)\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&(\,3x\,)^{2}+\{\,(\,-5\,)+(\,-4\,)\} \times 3x+ \{(\,-5\,) \times (\,-4\,)\}\\[6pt]&=&9x^{2}-27x+20\end{eqnarray}\;\;$

答$9x^{2}-27x+20$

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

$\;\;\begin{eqnarray}&=&(\,5x\,)^{2}+\{\,5+(-1)\} \times 5x+\{\,5 \times (\,-1\,)\}\\[6pt]&=&25x^{2}+20x-5\end{eqnarray}\;\;$

答$25x^{2}+20x-5$

(4) $\quad\;\,\begin{eqnarray}(\,-x+2\,)(\,-x-6\,)\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&(\,-x\,)^{2}+\{\,2+(\,-6\,)\} \times (\,-x\,)+\{\,2 \times (\,-6\,)\}\\[6pt]&=&x^{2}+4x-12\end{eqnarray}\;\;$

《 別解 》

$\quad\;\;\;\begin{eqnarray}(\,-x+2\,)(\,-x-6\,)\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&\{-(\,x-2\,)\}\{-(\,x+6\,)\}\\[6pt]&=&(\,x-2\,)(\,x+6\,)\\[6pt]&=&x^{2}+\{(\,-2\,)+6\,\} \times x+\{(\,-2\,) \times 6\}\\[6pt]&=&x^{2}+4x-12\end{eqnarray}\;\;$

答$x^{2}+4x-12$

(5) $\quad\;\,\begin{eqnarray}(\,8-4x\,)(\,7-4x\,)\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&(\,-4x+8\,)(\,-4x+7\,)\\[6pt]&=&(\,-4x\,)^{2}+(\,8+7\,) \times (\,-4x\,)+(\,8 \times 7\,)\\[6pt]&=&16x^{2}-60x+56\end{eqnarray}\;\;$

《 別解 》

$\quad\;\;\;\begin{eqnarray}(\,8-4x\,)(\,7-4x\,)\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&(\,-4x+8\,)(\,-4x+7\,)\\[6pt]&=&\{-(\,4x-8\,)\}\{-(\,4x-7\,)\}\\[6pt]&=&(\,4x-8\,)(\,4x-7\,)\\[6pt]&=&(\,4x\,)^{2}+\{(\,-8\,)+(\,-7\,)\} \times 4x+\{(\,-8\,) \times (\,-7\,)\}\\[6pt]&=&16x^{2}-60x+56\end{eqnarray}\;\;$

答$16x^{2}-60x+56$