Answer
$$(s+1-i)(s+1+i)(s+5)=-i^2s+s^3-5i^2+7s^2+11s+5$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(s+1-i)(s+1+i)(s+5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(-i^2+s^2+2s+1)(s+5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-i^2s+s^3-5i^2+7s^2+11s+5\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{s+1-i}\right) $ by each term in $ \left( s+1+i\right) $. $$ \left( \color{blue}{s+1-i}\right) \cdot \left( s+1+i\right) = \\ = s^2+s+ \cancel{is}+s+1+ \cancel{i} -\cancel{is} -\cancel{i}-i^2 $$ |
| ② | Combine like terms: $$ s^2+ \color{blue}{s} + \, \color{red}{ \cancel{is}} \,+ \color{blue}{s} +1+ \, \color{orange}{ \cancel{i}} \, \, \color{red}{ -\cancel{is}} \, \, \color{orange}{ -\cancel{i}} \,-i^2 = -i^2+s^2+ \color{blue}{2s} +1 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{-i^2+s^2+2s+1}\right) $ by each term in $ \left( s+5\right) $. $$ \left( \color{blue}{-i^2+s^2+2s+1}\right) \cdot \left( s+5\right) = -i^2s-5i^2+s^3+5s^2+2s^2+10s+s+5 $$ |
| ④ | Combine like terms: $$ -i^2s-5i^2+s^3+ \color{blue}{5s^2} + \color{blue}{2s^2} + \color{red}{10s} + \color{red}{s} +5 = -i^2s+s^3-5i^2+ \color{blue}{7s^2} + \color{red}{11s} +5 $$ |
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