Question
Answer
$$(1+s)^2\cdot(1-0.001s)=s^2+2s+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(1+s)^2\cdot(1-0.001s)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(1+2s+s^2)\cdot(1-0.001s) \xlongequal{ } \\[1 em] & \xlongequal{ }(1+2s+s^2)\cdot(1-0s) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}1+0s+2s+0s^2+s^2+0s^3 \xlongequal{ } \\[1 em] & \xlongequal{ }10s+2s0s^2+s^20s^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}s^2+2s+1\end{aligned} $$ | |
| ① | Find $ \left(1+s\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 1 } $ and $ B = \color{red}{ s }$. $$ \begin{aligned}\left(1+s\right)^2 = \color{blue}{1^2} +2 \cdot 1 \cdot s + \color{red}{s^2} = 1+2s+s^2\end{aligned} $$ |
| ② | Multiply each term of $ \left( \color{blue}{1+2s+s^2}\right) $ by each term in $ \left( 10s\right) $. $$ \left( \color{blue}{1+2s+s^2}\right) \cdot \left( 10s\right) = 10s+2s0s^2+s^20s^3 $$ |
| ③ | Combine like terms: $$ 1 \color{blue}{0s} + \color{blue}{2s} \color{red}{0s^2} + \color{red}{s^2} 0s^3 = \color{red}{s^2} + \color{blue}{2s} +1 $$ |
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