Answer
$$(s+1)(s+0.1)(s+10)(s+20)=s^4+31s^3+230s^2+200s$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(s+1)(s+0.1)(s+10)(s+20)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(1s^2+0s+s+0)(s+10)(s+20) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(1s^2+s)(s+10)(s+20) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(1s^3+10s^2+s^2+10s)(s+20) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(1s^3+11s^2+10s)(s+20) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}s^4+20s^3+11s^3+220s^2+10s^2+200s \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}s^4+31s^3+230s^2+200s\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{s+1}\right) $ by each term in $ \left( s0\right) $. $$ \left( \color{blue}{s+1}\right) \cdot \left( s0\right) = s^20s+s0 $$ |
| ② | Combine like terms: $$ s^2 \color{blue}{0s} + \color{blue}{s} 0 = s^2+ \color{blue}{s} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{s^2+s}\right) $ by each term in $ \left( s+10\right) $. $$ \left( \color{blue}{s^2+s}\right) \cdot \left( s+10\right) = s^3+10s^2+s^2+10s $$ |
| ④ | Combine like terms: $$ s^3+ \color{blue}{10s^2} + \color{blue}{s^2} +10s = s^3+ \color{blue}{11s^2} +10s $$ |
| ⑤ | Multiply each term of $ \left( \color{blue}{s^3+11s^2+10s}\right) $ by each term in $ \left( s+20\right) $. $$ \left( \color{blue}{s^3+11s^2+10s}\right) \cdot \left( s+20\right) = s^4+20s^3+11s^3+220s^2+10s^2+200s $$ |
| ⑥ | Combine like terms: $$ s^4+ \color{blue}{20s^3} + \color{blue}{11s^3} + \color{red}{220s^2} + \color{red}{10s^2} +200s = s^4+ \color{blue}{31s^3} + \color{red}{230s^2} +200s $$ |
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