Question
Answer
$$(s+2)(s+6)(s^2+4s+8)=s^4+12s^3+52s^2+112s+96$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(s+2)(s+6)(s^2+4s+8)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(1s^2+6s+2s+12)(s^2+4s+8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(1s^2+8s+12)(s^2+4s+8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}s^4+12s^3+52s^2+112s+96\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{s+2}\right) $ by each term in $ \left( s+6\right) $. $$ \left( \color{blue}{s+2}\right) \cdot \left( s+6\right) = s^2+6s+2s+12 $$ |
| ② | Combine like terms: $$ s^2+ \color{blue}{6s} + \color{blue}{2s} +12 = s^2+ \color{blue}{8s} +12 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{s^2+8s+12}\right) $ by each term in $ \left( s^2+4s+8\right) $. $$ \left( \color{blue}{s^2+8s+12}\right) \cdot \left( s^2+4s+8\right) = s^4+4s^3+8s^2+8s^3+32s^2+64s+12s^2+48s+96 $$ |
| ④ | Combine like terms: $$ s^4+ \color{blue}{4s^3} + \color{red}{8s^2} + \color{blue}{8s^3} + \color{green}{32s^2} + \color{orange}{64s} + \color{green}{12s^2} + \color{orange}{48s} +96 = \\ = s^4+ \color{blue}{12s^3} + \color{green}{52s^2} + \color{orange}{112s} +96 $$ |
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