Multiply $ \dfrac{3}{10} $ by $ s^2 $ to get $ \dfrac{ 3s^2 }{ 10 } $.

Step 1: Write $ s^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{3}{10} \cdot s^2 & \xlongequal{\text{Step 1}} \frac{3}{10} \cdot \frac{s^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 3 \cdot s^2 }{ 10 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3s^2 }{ 10 } \end{aligned} $$

Subtract $ \dfrac{3s^2}{10} $ from $ 10s $ to get $ \dfrac{ \color{purple}{ -3s^2+100s } }{ 10 }$.

Step 1: Write $ 10s $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 10 }$.

$$ \begin{aligned} 10s- \frac{3s^2}{10} & \xlongequal{\text{Step 1}} \frac{10s}{\color{red}{1}} - \frac{3s^2}{10} = \frac{ 10s \cdot \color{blue}{ 10 }}{ 1 \cdot \color{blue}{ 10 }} - \frac{ 3s^2 }{ 10 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 100s } }{ 10 } - \frac{ \color{purple}{ 3s^2 } }{ 10 }=\frac{ \color{purple}{ -3s^2+100s } }{ 10 } \end{aligned} $$

Subtract $3$ from $ \dfrac{-3s^2+100s}{10} $ to get $ \dfrac{ \color{purple}{ -3s^2+100s-30 } }{ 10 }$.

Step 1: Write $ 3 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{10}$.

$$ \begin{aligned} \frac{-3s^2+100s}{10} -3 & \xlongequal{\text{Step 1}} \frac{-3s^2+100s}{10} - \frac{3}{\color{red}{1}} = \frac{ -3s^2+100s }{ 10 } - \frac{ 3 \cdot \color{blue}{ 10 }}{ 1 \cdot \color{blue}{ 10 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -3s^2+100s } }{ 10 } - \frac{ \color{purple}{ 30 } }{ 10 }=\frac{ \color{purple}{ -3s^2+100s-30 } }{ 10 } \end{aligned} $$