32033中３・多項式の因数分解・計算問題・因数分解の公式2-3

(1) $\quad\;\,\begin{eqnarray}x^{2}+10xy+25y^{2}\end{eqnarray}$

$\;\;\begin{eqnarray}&=&x^{2}+2 \times \color{red}5y\color{black} \times x+\color{red}(\,5y\,)\color{black}^{2}\\[6pt]&=&(\,x+5y\,)^{2}\end{eqnarray}\;\;$

答$(\,x+5y\,)^{2}$

(2) $\quad\;\,\begin{eqnarray}x^{2}-16xy+64y^{2}\end{eqnarray}$

$\;\;\begin{eqnarray}&=&x^{2}\color{red}-\color{black}2 \times \color{red}8y\color{black} \times x+\color{red}(\,8y\,)\color{black}^{2}\\[6pt]&=&(\,x-8y\,)^{2}\end{eqnarray}\;\;$

答$(\,x-8y\,)^{2}$

(3) $\quad\;\,\begin{eqnarray}4a^{2}+12ab+9b^{2}\end{eqnarray}$

$\;\;\begin{eqnarray}&=&(\,2a\,)^{2}+2 \times \color{red}3b\color{black} \times 2a+\color{red}(\,3b\,)\color{black}^{2}\\[6pt]&=&(\,2a+3b\,)^{2}\end{eqnarray}\;\;$

答$(\,2a+3b\,)^{2}$

(4) $\quad\;\,\begin{eqnarray}16x^{2}-40xy+25y^{2}\end{eqnarray}\;\;$

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

答$(\,4x-5y\,)^{2}$

(5) $\quad\;\,\begin{eqnarray}100a^{2}-260ab+169b^{2}\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&(\,10a\,)^{2} \color{red}-\color{black} 2 \times \color{red}13b\color{black} \times 10a+\color{red}(\,13b\,)\color{black}^{2}\\[6pt]&=&(\,10a-13b\,)^{2}\end{eqnarray}\;\;$

答$(\,10a-13b\,)^{2}$