Answer
$$(s+5)^4=s^4+20s^3+150s^2+500s+625$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(s+5)^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}s^4+20s^3+150s^2+500s+625\end{aligned} $$ | |
| ① | $$ (s+5)^4 = (s+5)^2 \cdot (s+5)^2 $$ |
| ② | Find $ \left(s+5\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ s } $ and $ B = \color{red}{ 5 }$. $$ \begin{aligned}\left(s+5\right)^2 = \color{blue}{s^2} +2 \cdot s \cdot 5 + \color{red}{5^2} = s^2+10s+25\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{s^2+10s+25}\right) $ by each term in $ \left( s^2+10s+25\right) $. $$ \left( \color{blue}{s^2+10s+25}\right) \cdot \left( s^2+10s+25\right) = s^4+10s^3+25s^2+10s^3+100s^2+250s+25s^2+250s+625 $$ |
| ④ | Combine like terms: $$ s^4+ \color{blue}{10s^3} + \color{red}{25s^2} + \color{blue}{10s^3} + \color{green}{100s^2} + \color{orange}{250s} + \color{green}{25s^2} + \color{orange}{250s} +625 = \\ = s^4+ \color{blue}{20s^3} + \color{green}{150s^2} + \color{orange}{500s} +625 $$ |
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