32032中３・多項式の因数分解・計算問題・因数分解の公式2-2

(1) $\quad\;\,\begin{eqnarray}4x^{2}+8x+4\end{eqnarray}$

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

答$(\,2x+2\,)^{2}$

(2) $\quad\;\,\begin{eqnarray}9x^{2}-24x+16\end{eqnarray}$

$\;\;\begin{eqnarray}&=&(\,3x\,)^{2}\color{red}-\color{black}2 \times \color{red}4\color{black} \times 3x+\color{red}4\color{black}^{2}\\[6pt]&=&(\,3x-4\,)^{2}\end{eqnarray}\;\;$

答$(\,3x-4\,)^{2}$

(3) $\quad\;\,\begin{eqnarray}25a^{2}+60a+36\end{eqnarray}$

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

答$(\,5a+6\,)^{2}$

(4) $\quad\;\,\begin{eqnarray}100x^{2}-140x+49\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&(\,10x\,)^{2} \color{red}-\color{black} 2 \times \color{red}7\color{black} \times 10x+\color{red}7\color{black}^{2}\\[6pt]&=&(\,10x-7\,)^{2}\end{eqnarray}\;\;$

答$(\,10x-7\,)^{2}$

(5) $\quad\;\,\begin{eqnarray}144a^{2}-72a+9\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&(\,12a\,)^{2} \color{red}-\color{black} 2 \times \color{red}3\color{black} \times 12a+\color{red}3\color{black}^{2}\\[6pt]&=&(\,12a-3\,)^{2}\end{eqnarray}\;\;$

答$(\,12a-3\,)^{2}$