31033中３・多項式の展開・計算問題・展開の公式2-3

(1) $\quad\;\,\begin{eqnarray}(\,2x+3y\,)^{2}\end{eqnarray}$

$\;\;\begin{eqnarray}&=&(\,2x\,)^{2}+2\times 3y \times 2x + (\,3y\,)^{2}\\[6pt]&=&4x^{2}+12xy+9y^{2}\end{eqnarray}\;\;$

答$4x^{2}+12xy+9y^{2}$

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

$\;\;\begin{eqnarray}&=&(\,6x\,)^{2}+2\times 2y \times 6x + (\,2y\,)^{2}\\[6pt]&=&36x^{2}+24xy+4y^{2}\end{eqnarray}\;\;$

答$36x^{2}+24xy+4y^{2}$

(3) $\quad\;\,\begin{eqnarray}(\,0.5x+5y\,)^{2}\end{eqnarray}$

$\;\;\begin{eqnarray}&=&(\,0.5x\,)^{2}+2\times 5y \times 0.5x + (\,5y\,)^{2}\\[6pt]&=&0.25x^{2}+5xy+25y^{2}\end{eqnarray}\;\;$

答$0.25x^{2}+5xy+25y^{2}$

(4) $\quad\;\,\begin{eqnarray}(\,3x-4y\,)^{2}\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&(\,3x\,)^{2}-2\times 4y \times 3x + (\,4y\,)^{2}\\[6pt]&=&9x^{2}-24xy+16y^{2}\end{eqnarray}\;\;$

答$9x^{2}-24xy+16y^{2}$

(5) $\quad\;\,\begin{eqnarray}\Bigl(\,6x-\dfrac{5}{\;2\;}y\,\Bigr)^{2}\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&(\,6x\,)^{2}-2\times \dfrac{\;5\;}{\;2\;}y \times 6x +\Bigl(\,\dfrac{5}{\;2\;}y\,\Bigr)^{2}\\[6pt]&=&36x^{2}- 30xy +\dfrac{\;25\;}{\;4\;}y\end{eqnarray}\;\;$

答$36x^{2}- 30xy +\dfrac{\;25\;}{\;4\;}y$

(6) $\quad\;\,\begin{eqnarray}\Bigl(\dfrac{\;1\;}{\;5\;}x-\dfrac{1}{\;4\;}y\,\Bigr)^{2}\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&\Bigl(\dfrac{\;1\;}{\;5\;}x\,\Bigr)^{2}-2 \times \dfrac{1}{\;4\;}y \times \dfrac{\;1\;}{\;5\;}x + \Bigl(\dfrac{\;1\;}{\;4\;}y\,\Bigr)^{2}\\[6pt]&=&\dfrac{\;1\;}{\;25\;}x^{2}- \dfrac{1}{\;10\;}xy + \dfrac{\;1\;}{\;16\;}y^{2}\end{eqnarray}\;\;$

答$\dfrac{\;1\;}{\;25\;}x^{2}- \dfrac{1}{\;10\;}xy + \dfrac{\;1\;}{\;16\;}y^{2}$