Question
Answer
$$20(s+2)(s+3)(s+6)(s+8)=20s^4+380s^3+2480s^2+6480s+5760$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}20(s+2)(s+3)(s+6)(s+8)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(20s+40)(s+3)(s+6)(s+8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(20s^2+60s+40s+120)(s+6)(s+8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(20s^2+100s+120)(s+6)(s+8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(20s^3+120s^2+100s^2+600s+120s+720)(s+8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}(20s^3+220s^2+720s+720)(s+8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}20s^4+380s^3+2480s^2+6480s+5760\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{20} $ by $ \left( s+2\right) $ $$ \color{blue}{20} \cdot \left( s+2\right) = 20s+40 $$ |
| ② | Multiply each term of $ \left( \color{blue}{20s+40}\right) $ by each term in $ \left( s+3\right) $. $$ \left( \color{blue}{20s+40}\right) \cdot \left( s+3\right) = 20s^2+60s+40s+120 $$ |
| ③ | Combine like terms: $$ 20s^2+ \color{blue}{60s} + \color{blue}{40s} +120 = 20s^2+ \color{blue}{100s} +120 $$ |
| ④ | Multiply each term of $ \left( \color{blue}{20s^2+100s+120}\right) $ by each term in $ \left( s+6\right) $. $$ \left( \color{blue}{20s^2+100s+120}\right) \cdot \left( s+6\right) = 20s^3+120s^2+100s^2+600s+120s+720 $$ |
| ⑤ | Combine like terms: $$ 20s^3+ \color{blue}{120s^2} + \color{blue}{100s^2} + \color{red}{600s} + \color{red}{120s} +720 = 20s^3+ \color{blue}{220s^2} + \color{red}{720s} +720 $$ |
| ⑥ | Multiply each term of $ \left( \color{blue}{20s^3+220s^2+720s+720}\right) $ by each term in $ \left( s+8\right) $. $$ \left( \color{blue}{20s^3+220s^2+720s+720}\right) \cdot \left( s+8\right) = 20s^4+160s^3+220s^3+1760s^2+720s^2+5760s+720s+5760 $$ |
| ⑦ | Combine like terms: $$ 20s^4+ \color{blue}{160s^3} + \color{blue}{220s^3} + \color{red}{1760s^2} + \color{red}{720s^2} + \color{green}{5760s} + \color{green}{720s} +5760 = \\ = 20s^4+ \color{blue}{380s^3} + \color{red}{2480s^2} + \color{green}{6480s} +5760 $$ |
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