Question
Answer
$$(s-8)(s-2)(s+3)=s^3-7s^2-14s+48$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(s-8)(s-2)(s+3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(1s^2-2s-8s+16)(s+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(1s^2-10s+16)(s+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}s^3+3s^2-10s^2-30s+16s+48 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}s^3-7s^2-14s+48\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{s-8}\right) $ by each term in $ \left( s-2\right) $. $$ \left( \color{blue}{s-8}\right) \cdot \left( s-2\right) = s^2-2s-8s+16 $$ |
| ② | Combine like terms: $$ s^2 \color{blue}{-2s} \color{blue}{-8s} +16 = s^2 \color{blue}{-10s} +16 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{s^2-10s+16}\right) $ by each term in $ \left( s+3\right) $. $$ \left( \color{blue}{s^2-10s+16}\right) \cdot \left( s+3\right) = s^3+3s^2-10s^2-30s+16s+48 $$ |
| ④ | Combine like terms: $$ s^3+ \color{blue}{3s^2} \color{blue}{-10s^2} \color{red}{-30s} + \color{red}{16s} +48 = s^3 \color{blue}{-7s^2} \color{red}{-14s} +48 $$ |
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