Answer
$$10(s+0.1)(s+6)k=10ks^2+60ks$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}10(s+0.1)(s+6)k& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(10s+0)(s+6)k \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(10s^2+60s+0s+0)k \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(10s^2+60s)k \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}10ks^2+60ks\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{10} $ by $ \left( s0\right) $ $$ \color{blue}{10} \cdot \left( s0\right) = 10s0 $$ |
| ② | Multiply each term of $ \left( \color{blue}{10s0}\right) $ by each term in $ \left( s+6\right) $. $$ \left( \color{blue}{10s0}\right) \cdot \left( s+6\right) = 10s^2+60s0s0 $$ |
| ③ | Combine like terms: $$ 10s^2+ \color{blue}{60s} \color{blue}{0s} 0 = 10s^2+ \color{blue}{60s} $$ |
| ④ | $$ \left( \color{blue}{10s^2+60s}\right) \cdot k = 10ks^2+60ks $$ |
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