Question
Answer
$$\dfrac{100(s+1)(s+10)}{s^3}=\dfrac{100s^2+1100s+1000}{s^3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{100(s+1)(s+10)}{s^3}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{(100s+100)(s+10)}{s^3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{100s^2+1000s+100s+1000}{s^3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{100s^2+1100s+1000}{s^3}\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{100} $ by $ \left( s+1\right) $ $$ \color{blue}{100} \cdot \left( s+1\right) = 100s+100 $$ |
| ② | Multiply each term of $ \left( \color{blue}{100s+100}\right) $ by each term in $ \left( s+10\right) $. $$ \left( \color{blue}{100s+100}\right) \cdot \left( s+10\right) = 100s^2+1000s+100s+1000 $$ |
| ③ | Simplify numerator $$ 100s^2+ \color{blue}{1000s} + \color{blue}{100s} +1000 = 100s^2+ \color{blue}{1100s} +1000 $$ |
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