31043中３・多項式の展開・計算問題・展開の公式3-3

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

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

答$9x^{2}-y^{2}$

(2) $\quad\;\,\begin{eqnarray}(\,6x-7y\,)(\,6x+7y\,)\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&(\,6x\,)^{2}-(\,7y\,)^{2}\\[6pt]&=&36x^{2}-49y^{2}\end{eqnarray}\;\;$

答$36x^{2}-49y^{2}$

(3) $\quad\;\,\begin{eqnarray}(\,8a-2b\,)(\,2b+8a\,)\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&(\,8a-2b\,)(\,8a+2b\,)\\[6pt]&=&(\,8a\,)^{2}-(\,2b\,)^{2}\\[6pt]&=&64a^{2}-4b^{2}\end{eqnarray}\;\;$

答$64a^{2}-4b^{2}$

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

$\;\;\begin{eqnarray}&=&(\,-2x-5y\,)(\,-2x+5y\,)\\[6pt]&=&(\,-2x\,)^{2}-(\,5y\,)^{2}\\[6pt]&=&4x^{2}-25y^{2}\end{eqnarray}\;\;$

答$4x^{2}-25y^{2}$

(5) $\quad\;\,\begin{eqnarray}(\,-0.3a+0.3b\,)(\,0.3b+0.3a\,)\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&(\,0.3b-0.3a\,)(\,0.3b+0.3a\,)\\[6pt]&=&(\,0.3b\,)^{2}-(\,0.3a\,)^{2}\\[6pt]&=&0.09b^{2}-0.09a^{2}\end{eqnarray}\;\;$

答$0.09b^{2}-0.09a^{2}$

(6) $\quad\;\,\begin{eqnarray}\Bigl(\,\dfrac{\;5\;}{\;6\;}x+\dfrac{3}{\;4\;}y\,\Bigr)\Bigl(\,\dfrac{\;5\;}{\;6\;}x-\dfrac{3}{\;4\;}y\,\Bigr)\end{eqnarray}$

$\;\;\begin{eqnarray}&=&\Bigl(\,\frac{5}{\;6\;}x\,\Bigr)^{2}-\Bigl(\,\frac{3}{\;4\;}y\,\Bigr)^{2}\\[6pt]&=&\dfrac{\;25\;}{\;36\;}x^{2}-\dfrac{9}{\;16\;}y^{2}\end{eqnarray}\;\;$

答$\dfrac{\;25\;}{\;36\;}x^{2}-\dfrac{9}{\;16\;}y^{2}$