Answer
$$(0.3s+1)(3s+1)(0.45s+1)\cdot(1+10s)+0.6k\cdot(1-10s)=30s^2+13s+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(0.3s+1)(3s+1)(0.45s+1)\cdot(1+10s)+0.6k\cdot(1-10s)& \xlongequal{ }(0s+1)(3s+1)(0s+1)\cdot(1+10s)+0k\cdot(1-10s) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(0s^2+0s+3s+1)(0s+1)\cdot(1+10s)+0k+0ks \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(3s+1)(0s+1)\cdot(1+10s)+0k+0ks \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(0s^2+3s+0s+1)\cdot(1+10s)+0k+0ks \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(3s+1)\cdot(1+10s)+0k+0ks \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}3s+30s^2+1+10s+0k+0ks \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}30s^2+13s+1+0k+0ks \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}30s^2+13s+1\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{0s+1}\right) $ by each term in $ \left( 3s+1\right) $. $$ \left( \color{blue}{0s+1}\right) \cdot \left( 3s+1\right) = 0s^20s+3s+1 $$Multiply $ \color{blue}{0k} $ by $ \left( 1-10s\right) $ $$ \color{blue}{0k} \cdot \left( 1-10s\right) = 0k0ks $$ |
| ② | Combine like terms: $$ 0s^2 \color{blue}{0s} + \color{blue}{3s} +1 = \color{blue}{3s} +1 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{3s+1}\right) $ by each term in $ \left( 0s+1\right) $. $$ \left( \color{blue}{3s+1}\right) \cdot \left( 0s+1\right) = 0s^2+3s0s+1 $$ |
| ④ | Combine like terms: $$ 0s^2+ \color{blue}{3s} \color{blue}{0s} +1 = \color{blue}{3s} +1 $$ |
| ⑤ | Multiply each term of $ \left( \color{blue}{3s+1}\right) $ by each term in $ \left( 1+10s\right) $. $$ \left( \color{blue}{3s+1}\right) \cdot \left( 1+10s\right) = 3s+30s^2+1+10s $$ |
| ⑥ | Combine like terms: $$ \color{blue}{3s} +30s^2+1+ \color{blue}{10s} = 30s^2+ \color{blue}{13s} +1 $$ |
| ⑦ | Combine like terms: $$ 30s^2+13s+10k0ks = 30s^2+13s+1 $$ |
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