31041中３・多項式の展開・計算問題・展開の公式3-1

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

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

答$x^{2}-9$

(2) $\quad\;\,\begin{eqnarray}(\,x-10\,)(\,x+10\,)\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&x^{2}-10^{2}\\[6pt]&=&x^{2}-100\end{eqnarray}\;\;$

答$x^{2}-100$

(3) $\quad\;\,\begin{eqnarray}(\,7+a\,)(\,7-a\,)\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&7^{2}-a^{2}\\[6pt]&=&49-a^{2}\end{eqnarray}\;\;$

答$49-a^{2}$

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

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

答$x^{2}-81$

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

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

答$x^{2}-0.16$

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

$\;\;\begin{eqnarray}&=&x^{2}-\Bigl(\,\frac{1}{\;6\;}\,\Bigr)^{2}\\[6pt]&=&x^{2}-\frac{1}{\;36\;}\end{eqnarray}\;\;$

答$x^{2}-\dfrac{1}{\;36\;}$