32043中３・多項式の因数分解・計算問題・因数分解の公式3-3
banno計算問題 》因数分解の公式３③
次の式を展開しなさい。
(1) $x^{2}-9y^{2}$
(2) $16x^{2}-25y^{2}$
(3) $144a^{2}-81b^{2}$
(4) $0.01x^{2}-y^{2}$
(5) $\dfrac{\;9\;}{\;4\;}a^{2}-\dfrac{\;1\;}{\;49\;}b^{2}$
解答・解説
(1) $\quad\;\,\begin{eqnarray}x^{2}-9y^{2}\end{eqnarray}\;\;$
$\;\;\begin{eqnarray}&=&x^{2}-(\,3y\,)^{2}\\[6pt]&=&(\,x+3y\,)(\,x-3y\,)\end{eqnarray}\;\;$
答$(\,x+3y\,)(\,x-3y\,)$
(2) $\quad\;\,\begin{eqnarray}16x^{2}-25y^{2}\end{eqnarray}\;\;$
$\;\;\begin{eqnarray}&=&(\,4x\,)^{2}-(\,5y\,)^{2}\\[6pt]&=&(\,4x+5y\,)(\,4x-5y\,)\end{eqnarray}\;\;$
答$(\,4x+5y\,)(\,4x-5y\,)$
(3) $\quad\;\,\begin{eqnarray}144a^{2}-81b^{2}\end{eqnarray}\;\;$
$\;\;\begin{eqnarray}&=&(\,12a\,)^{2}-(\,9b\,)^{2}\\[6pt]&=&(\,12a+9b\,)(\,12a-9b\,)\end{eqnarray}\;\;$
答$(\,12a+9b\,)(\,12a-9b\,)$
(4) $\quad\;\,\begin{eqnarray}0.01x^{2}-y^{2}\end{eqnarray}\;\;$
$\;\;\begin{eqnarray}&=&(\,0.1x\,)^{2}-y^{2}\\[6pt]&=&(\,0.1x+y\,)(\,0.1x-y\,)\end{eqnarray}\;\;$
答$(\,0.1x+y\,)(\,0.1x-y\,)$
(5) $\quad\;\,\begin{eqnarray}\dfrac{\;9\;}{\;4\;}a^{2}-\dfrac{\;1\;}{\;49\;}b^{2}\end{eqnarray}\;\;$
$\;\;\begin{eqnarray}&=&\Bigl(\,\dfrac{3}{\;2\;}a\,\Bigr)^{2}-\Bigl(\,\dfrac{1}{\;7\;}b\,\Bigr)^{2}\\[6pt]&=&\Bigl(\,\dfrac{3}{\;2\;}a+\dfrac{1}{\;7\;}b\,\Bigr)\Bigl(\,\dfrac{3}{\;2\;}a-\dfrac{1}{\;7\;}b\,\Bigr)\end{eqnarray}\;\;$
答$\Bigl(\,\dfrac{3}{\;2\;}a+\dfrac{1}{\;7\;}b\,\Bigr)\Bigl(\,\dfrac{3}{\;2\;}a-\dfrac{1}{\;7\;}b\,\Bigr)$
