Question
Answer
$$(s+1)(s+2)(s+10)=s^3+13s^2+32s+20$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(s+1)(s+2)(s+10)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(1s^2+2s+s+2)(s+10) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(1s^2+3s+2)(s+10) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}s^3+10s^2+3s^2+30s+2s+20 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}s^3+13s^2+32s+20\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{s+1}\right) $ by each term in $ \left( s+2\right) $. $$ \left( \color{blue}{s+1}\right) \cdot \left( s+2\right) = s^2+2s+s+2 $$ |
| ② | Combine like terms: $$ s^2+ \color{blue}{2s} + \color{blue}{s} +2 = s^2+ \color{blue}{3s} +2 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{s^2+3s+2}\right) $ by each term in $ \left( s+10\right) $. $$ \left( \color{blue}{s^2+3s+2}\right) \cdot \left( s+10\right) = s^3+10s^2+3s^2+30s+2s+20 $$ |
| ④ | Combine like terms: $$ s^3+ \color{blue}{10s^2} + \color{blue}{3s^2} + \color{red}{30s} + \color{red}{2s} +20 = s^3+ \color{blue}{13s^2} + \color{red}{32s} +20 $$ |
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