数式の計算

■問題

次の計算をしなさい．

$3$\displaystyle{\displaystyle{{ \left({ s+\frac{\hspace{2}2\hspace{2}}{\hspace{2}3\hspace{2}}t- \frac{\hspace{2}5\hspace{2}}{\hspace{2}4\hspace{2}}u }\right) }^{2}}}$

■答

$3$\displaystyle{ {s}^{2}+\frac{\hspace{2}4\hspace{2}}{\hspace{2}9\hspace{2}}{t}^{2}+\frac{\hspace{2} 25 \hspace{2}}{\hspace{2} 16 \hspace{2}}{u}^{2}+\frac{\hspace{2}4\hspace{2}}{\hspace{2}3\hspace{2}}st- \frac{\hspace{2}5\hspace{2}}{\hspace{2}3\hspace{2}}tu- \frac{\hspace{2}5\hspace{2}}{\hspace{2}2\hspace{2}}us }$

■ヒント

次の公式を用いる

$3$\displaystyle{ { $x+y- z$ }^{2} }$ $3$\displaystyle{ ={x}^{2}+{y}^{2}+{ $- z$ }^{2}+2xy+2y$- z$+2$- z$x }$

$3$\displaystyle{ ={x}^{2}+{y}^{2}+{z}^{2}+2xy- 2yz- 2zx }$

■答

$3$\displaystyle{\displaystyle{{ \left({ s+\frac{\hspace{2}2\hspace{2}}{\hspace{2}3\hspace{2}}t- \frac{\hspace{2}5\hspace{2}}{\hspace{2}4\hspace{2}}u }\right) }^{2}}}$

$3$\displaystyle{={s}^{2}+{ \left({ \frac{\hspace{2}2\hspace{2}}{\hspace{2}3\hspace{2}}t }\right) }^{2}+{\left({ - \frac{\hspace{2}5\hspace{2}}{\hspace{2}4\hspace{2}}u }\right)}^{2}}$ $3$\displaystyle{+2\times s\times \frac{\hspace{2}2\hspace{2}}{\hspace{2}3\hspace{2}}t}$ $3$\displaystyle{+2\times \frac{\hspace{2}2\hspace{2}}{\hspace{2}3\hspace{2}}t\times \left({ - \frac{\hspace{2}5\hspace{2}}{\hspace{2}4\hspace{2}}u }\right)}$ $3$\displaystyle{+2\times \left({ - \frac{\hspace{2}5\hspace{2}}{\hspace{2}4\hspace{2}}u }\right)\times s}$

同類項をまとめる

$3$\displaystyle{ ={s}^{2}+\frac{\hspace{2}4\hspace{2}}{\hspace{2}9\hspace{2}}{t}^{2}+\frac{\hspace{2} 25 \hspace{2}}{\hspace{2} 16 \hspace{2}}{u}^{2}+\frac{\hspace{2}4\hspace{2}}{\hspace{2}3\hspace{2}}st- \frac{\hspace{2}5\hspace{2}}{\hspace{2}3\hspace{2}}tu- \frac{\hspace{2}5\hspace{2}}{\hspace{2}2\hspace{2}}us }$

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最終更新日： 2023年7月19日