Multiply $4$ by $ \dfrac{a^2}{10} $ to get $ \dfrac{ 4a^2 }{ 10 } $.

Step 1: Write $ 4 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 4 \cdot \frac{a^2}{10} & \xlongequal{\text{Step 1}} \frac{4}{\color{red}{1}} \cdot \frac{a^2}{10} \xlongequal{\text{Step 2}} \frac{ 4 \cdot a^2 }{ 1 \cdot 10 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4a^2 }{ 10 } \end{aligned} $$

Multiply $ \dfrac{4a^2}{10} $ by $ a $ to get $ \dfrac{ 4a^3 }{ 10 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{4a^2}{10} \cdot a & \xlongequal{\text{Step 1}} \frac{4a^2}{10} \cdot \frac{a}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 4a^2 \cdot a }{ 10 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4a^3 }{ 10 } \end{aligned} $$

Subtract $ \dfrac{4a^3}{10} $ from $ 9 $ to get $ \dfrac{ \color{purple}{ -4a^3+90 } }{ 10 }$.

Step 1: Write $ 9 $ 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 $\color{blue}{ 10 }$.

$$ \begin{aligned} 9- \frac{4a^3}{10} & \xlongequal{\text{Step 1}} \frac{9}{\color{red}{1}} - \frac{4a^3}{10} = \frac{ 9 \cdot \color{blue}{ 10 }}{ 1 \cdot \color{blue}{ 10 }} - \frac{ 4a^3 }{ 10 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 90 } }{ 10 } - \frac{ \color{purple}{ 4a^3 } }{ 10 }=\frac{ \color{purple}{ -4a^3+90 } }{ 10 } \end{aligned} $$

Subtract $15$ from $ \dfrac{-4a^3+90}{10} $ to get $ \dfrac{ \color{purple}{ -4a^3-60 } }{ 10 }$.

Step 1: Write $ 15 $ 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 $\color{blue}{10}$.

$$ \begin{aligned} \frac{-4a^3+90}{10} -15 & \xlongequal{\text{Step 1}} \frac{-4a^3+90}{10} - \frac{15}{\color{red}{1}} = \frac{ -4a^3+90 }{ 10 } - \frac{ 15 \cdot \color{blue}{ 10 }}{ 1 \cdot \color{blue}{ 10 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -4a^3+90 } }{ 10 } - \frac{ \color{purple}{ 150 } }{ 10 }=\frac{ \color{purple}{ -4a^3-60 } }{ 10 } \end{aligned} $$