31042中３・多項式の展開・計算問題・展開の公式3-2

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

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

答$4x^{2}-9$

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

$\;\;\begin{eqnarray}&=&(\,5x\,)^{2}-8^{2}\\[6pt]&=&25x^{2}-64\end{eqnarray}\;\;$

答$25x^{2}-64$

(3) $\quad\;\,\begin{eqnarray}(\,10+6a\,)(\,10-6a\,)\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&10^{2}-(\,6a\,)^{2}\\[6pt]&=&100-36a^{2}\end{eqnarray}\;\;$

答$100-36a^{2}$

(4) $\quad\;\,\begin{eqnarray}(\,-3x-9\,)(\,-3x+9\,)\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&(\,-3x\,)^{2}-9^{2}\\[6pt]&=&9x^{2}-81\end{eqnarray}\;\;$

答$9x^{2}-81$

(5) $\quad\;\,\begin{eqnarray}(\,0.4x-0.1\,)(\,0.4x+0.1\,)\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&(\,0.4x\,)^{2}-0.1^{2}\\[6pt]&=&0.16x^{2}-0.01\end{eqnarray}\;\;$

答$0.16x^{2}-0.01$

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

$\;\;\begin{eqnarray}&=&\Bigl(\,\frac{1}{\;2\;}x\,\Bigr)^{2}-\Bigl(\,\frac{1}{\;3\;}\,\Bigr)^{2}\\[6pt]&=&\dfrac{\;1\;}{\;4\;}x^{2}-\dfrac{1}{\;9\;}\end{eqnarray}\;\;$

答$\dfrac{\;1\;}{\;4\;}x^{2}-\dfrac{1}{\;9\;}$