31031中３・多項式の展開・計算問題・展開の公式2-1

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

$\;\;\begin{eqnarray}&=&x^{2}+2\times 2\times x+2^{2}\\[6pt]&=&x^{2}+4x+4\end{eqnarray}\;\;$

答$x^{2}+4x+4$

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

$\;\;\begin{eqnarray}&=&x^{2}+2\times 10\times x+10^{2}\\[6pt]&=&x^{2}+20x+100\end{eqnarray}\;\;$

答$x^{2}+20x+100$

(3) $\quad\;\,\begin{eqnarray}(\,x+0.6\,)^{2}\end{eqnarray}$

$\;\;\begin{eqnarray}&=&x^{2}+2\times 0.6\times x+0.6^{2}\\[6pt]&=&x^{2}+1.2x+0.36\end{eqnarray}\;\;$

答$x^{2}+1.2x+0.36$

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

$\;\;\begin{eqnarray}&=&x^{2}-2\times 1\times x+1^{2}\\[6pt]&=&x^{2}-2x+1\end{eqnarray}\;\;$

答$x^{2}-2x+1$

(5) $\quad\;\,\begin{eqnarray}\Bigl(\,x-\frac{2}{3}\,\Bigr)^{2}\end{eqnarray}\;\;$

$\;\;\begin{eqnarray}&=&x^{2}-2\times \frac{2}{\;3\;}\times x +\Bigl(\,-\frac{2}{\;3\;}\,\Bigr)^{2}\\[6pt]&=&x^{2}-\frac{4}{\;3\;}x+\frac{4}{\;9\;}\end{eqnarray}\;\;$

答$x^{2}-\dfrac{4}{\;3\;}x+\dfrac{4}{\;9\;}$

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

$\;\;\begin{eqnarray}&=&4^{2}-2\times x\times 4+x^{2}\\[6pt]&=&16-8x+x^{2}\\[6pt]&=&x^{2}-8x+16\end{eqnarray}\;\;$

答$x^{2}-8x+16$