31053中３・多項式の展開・計算問題・いろいろな式の展開3

(1) $\quad\;\,\begin{eqnarray}(\,2x-y\,)(\,2x+y\,)-4(\,x-2y\,)(\,x+6y\,)\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&4x^{2}-y^{2}-4(\,x^{2}+4xy-12y^{2}\,)\\[6pt]&=&4x^{2}-y^{2}-4x^{2}-16xy+48y^{2}\\[6pt]&=&47y^{2}-16xy\end{eqnarray}\;\;$

答$47y^{2}-16xy$

(2) $\quad\;\,\begin{eqnarray}4(\,-2x-6y\,)^{2}-2(\,3x-4y\,)^{2}\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&4(\,4x^{2}+24xy+36y^{2}\,)-2(\,9x^{2}-24xy+16y^{2}\,)\\[6pt]&=&16x^{2}+96xy+144y^{2}-18x^{2}+48xy-32y^{2}\\[6pt]&=&-2x^{2}+144xy+112y^{2}\end{eqnarray}\;\;$

答$-2x^{2}+144xy+112y^{2}$

(3) $\quad\;\,\begin{eqnarray}5(\,0.4a+b\,)^{2}-20(\,0.2a-2b\,)(\,0.2a+3b\,)\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&5(\,0.16a^{2}+0.8ab+b^{2}\,)-20(\,0.04a^{2}+0.2ab-6b^{2}\,)\\[6pt]&=&0.8a^{2}+4ab+5b^{2}-0.8a^{2}-4ab+120b^{2}\\[6pt]&=&125b^{2}\end{eqnarray}\;\;$

答$125b^{2}$

(4) $\quad\;\,\begin{eqnarray}\Bigl(\,\dfrac{\;1\;}{\;3\;}x+2y\,\Bigr)\Bigl(\,\dfrac{\;1\;}{\;3\;}x+y\,\Bigr)-2\Bigl(\,3y+\dfrac{\;2\;}{\;3\;}x\,\Bigr)\Bigl(\,3y-\dfrac{\;2\;}{\;3\;}x\,\Bigr)\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&\dfrac{\;1\;}{\;9\;}x^{2}+xy+2y^{2}-2\Bigl(\,9y^{2}-\dfrac{\;4\;}{\;9\;}x^{2}\,\Bigr)\\[6pt]&=&\dfrac{\;1\;}{\;9\;}x^{2}+xy+2y^{2}-18y^{2}+\dfrac{\;8\;}{\;9\;}x^{2}\\[6pt]&=&x^{2}+xy-16y^{2}\end{eqnarray}\;\;$

答$x^{2}+xy-16y^{2}$