Use the distributive property.

Multiply $8$ by $ \dfrac{y^2}{10} $ to get $ \dfrac{ 8y^2 }{ 10 } $.

Step 1: Write $ 8 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 8 \cdot \frac{y^2}{10} & \xlongequal{\text{Step 1}} \frac{8}{\color{red}{1}} \cdot \frac{y^2}{10} \xlongequal{\text{Step 2}} \frac{ 8 \cdot y^2 }{ 1 \cdot 10 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 8y^2 }{ 10 } \end{aligned} $$

Subtract $ \dfrac{8y^2}{10} $ from $ 4 $ to get $ \dfrac{ \color{purple}{ -8y^2+40 } }{ 10 }$.

Step 1: Write $ 4 $ 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 $\color{blue}{ 10 }$.

$$ \begin{aligned} 4- \frac{8y^2}{10} & \xlongequal{\text{Step 1}} \frac{4}{\color{red}{1}} - \frac{8y^2}{10} = \frac{ 4 \cdot \color{blue}{ 10 }}{ 1 \cdot \color{blue}{ 10 }} - \frac{ 8y^2 }{ 10 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 40 } }{ 10 } - \frac{ \color{purple}{ 8y^2 } }{ 10 }=\frac{ \color{purple}{ -8y^2+40 } }{ 10 } \end{aligned} $$

Multiply $ \dfrac{-8y^2+40}{10} $ by $ y $ to get $ \dfrac{ -8y^3+40y }{ 10 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{-8y^2+40}{10} \cdot y & \xlongequal{\text{Step 1}} \frac{-8y^2+40}{10} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( -8y^2+40 \right) \cdot y }{ 10 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -8y^3+40y }{ 10 } \end{aligned} $$

Subtract $5$ from $ \dfrac{-8y^3+40y}{10} $ to get $ \dfrac{ \color{purple}{ -8y^3+40y-50 } }{ 10 }$.

Step 1: Write $ 5 $ 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 $\color{blue}{10}$.

$$ \begin{aligned} \frac{-8y^3+40y}{10} -5 & \xlongequal{\text{Step 1}} \frac{-8y^3+40y}{10} - \frac{5}{\color{red}{1}} = \frac{ -8y^3+40y }{ 10 } - \frac{ 5 \cdot \color{blue}{ 10 }}{ 1 \cdot \color{blue}{ 10 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -8y^3+40y } }{ 10 } - \frac{ \color{purple}{ 50 } }{ 10 }=\frac{ \color{purple}{ -8y^3+40y-50 } }{ 10 } \end{aligned} $$