Answer
$$(s-1)(s+3)(s+10)(s+1)=s^4+13s^3+29s^2-13s-30$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(s-1)(s+3)(s+10)(s+1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(1s^2+3s-s-3)(s+10)(s+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(1s^2+2s-3)(s+10)(s+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(1s^3+10s^2+2s^2+20s-3s-30)(s+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(1s^3+12s^2+17s-30)(s+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}s^4+13s^3+29s^2-13s-30\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{s-1}\right) $ by each term in $ \left( s+3\right) $. $$ \left( \color{blue}{s-1}\right) \cdot \left( s+3\right) = s^2+3s-s-3 $$ |
| ② | Combine like terms: $$ s^2+ \color{blue}{3s} \color{blue}{-s} -3 = s^2+ \color{blue}{2s} -3 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{s^2+2s-3}\right) $ by each term in $ \left( s+10\right) $. $$ \left( \color{blue}{s^2+2s-3}\right) \cdot \left( s+10\right) = s^3+10s^2+2s^2+20s-3s-30 $$ |
| ④ | Combine like terms: $$ s^3+ \color{blue}{10s^2} + \color{blue}{2s^2} + \color{red}{20s} \color{red}{-3s} -30 = s^3+ \color{blue}{12s^2} + \color{red}{17s} -30 $$ |
| ⑤ | Multiply each term of $ \left( \color{blue}{s^3+12s^2+17s-30}\right) $ by each term in $ \left( s+1\right) $. $$ \left( \color{blue}{s^3+12s^2+17s-30}\right) \cdot \left( s+1\right) = s^4+s^3+12s^3+12s^2+17s^2+17s-30s-30 $$ |
| ⑥ | Combine like terms: $$ s^4+ \color{blue}{s^3} + \color{blue}{12s^3} + \color{red}{12s^2} + \color{red}{17s^2} + \color{green}{17s} \color{green}{-30s} -30 = s^4+ \color{blue}{13s^3} + \color{red}{29s^2} \color{green}{-13s} -30 $$ |
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