32041中３・多項式の因数分解・計算問題・因数分解の公式3-1

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

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

答$(\,x+3\,)(\,x-3\,)$

(2) $\quad\;\,\begin{eqnarray}x^{2}-64\end{eqnarray}\;\;$

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

答$(\,x+8\,)(\,x-8\,)$

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

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

答$(\,a+11\,)(\,a-11\,)$

(4) $\quad\;\,\begin{eqnarray}81-x^{2}\end{eqnarray}\;\;$

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

答$(\,9+x\,)(\,9-x\,)$

(5) $\quad\;\,\begin{eqnarray}x^{2}-0.04\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&x^{2}-0.2^{2}\\[6pt]&=&(\,x-0.2\,)(\,x+0.2\,)\end{eqnarray}\;\;$

答$(\,x-0.2\,)(\,x+0.2\,)$

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

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

答$\Bigl(\,x+\dfrac{2}{\;5\;}\,\Bigr)\Bigl(\,x-\dfrac{2}{\;5\;}\,\Bigr)$