32031中３・多項式の因数分解・計算問題・因数分解の公式2-1

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

$\;\;\begin{eqnarray}&=&x^{2}+2 \times \color{red}1\color{black} \times x+\color{red}1\color{black}^{2}\\[6pt]&=&(\,x+1\,)^{2}\end{eqnarray}\;\;$

答$(\,x+1\,)^{2}$

(2) $\quad\;\,\begin{eqnarray}x^{2}+8x+16\end{eqnarray}$

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

答$(\,x+4\,)^{2}$

(3) $\quad\;\,\begin{eqnarray}x^{2}+12x+36\end{eqnarray}$

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

答$(\,x+6\,)^{2}$

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

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

答$(\,x-2\,)^{2}$

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

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

答$(\,x-8\,)^{2}$

(6) $\quad\;\,\begin{eqnarray}x^{2}-20x+100\end{eqnarray}\;\;$

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

答$(\,x-10\,)^{2}$