32042中３・多項式の因数分解・計算問題・因数分解の公式3-2

(1) $\quad\;\,\begin{eqnarray}4x^{2}-25\end{eqnarray}\;\;$

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

答$(\,2x+5\,)(\,2x-5\,)$

(2) $\quad\;\,\begin{eqnarray}9x^{2}-1\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&(\,3x\,)^{2}-1^{2}\\[6pt]&=&(\,3x+1\,)(\,3x-1\,)\end{eqnarray}\;\;$

答$(\,3x+1\,)(\,3x-1\,)$

(3) $\quad\;\,\begin{eqnarray}121a^{2}-100\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&(\,11a\,)^{2}-10^{2}\\[6pt]&=&(\,11a+10\,)(\,11a-10\,)\end{eqnarray}\;\;$

答$(\,11a+10\,)(\,11a-10\,)$

(4) $\quad\;\,\begin{eqnarray}49-16x^{2}\end{eqnarray}\;\;$

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

答$(\,7+4x\,)(\,7-4x\,)$

(5) $\quad\;\,\begin{eqnarray}\dfrac{\;1\;}{\;36\;}x^{2}-\dfrac{\;1\;}{\;25\;}\end{eqnarray}\;\;$

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

答$\Bigl(\,\dfrac{1}{\;6\;}x+\dfrac{1}{\;5\;}\,\Bigr)\Bigl(\,\dfrac{1}{\;6\;}x-\dfrac{1}{\;5\;}\,\Bigr)$