Use the distributive property.

Multiply $15$ by $ \dfrac{x}{10} $ to get $ \dfrac{ 15x }{ 10 } $.

Step 1: Write $ 15 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 15 \cdot \frac{x}{10} & \xlongequal{\text{Step 1}} \frac{15}{\color{red}{1}} \cdot \frac{x}{10} \xlongequal{\text{Step 2}} \frac{ 15 \cdot x }{ 1 \cdot 10 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 15x }{ 10 } \end{aligned} $$

Subtract $ \dfrac{15x}{10} $ from $ 5 $ to get $ \dfrac{ \color{purple}{ -15x+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 first fraction by $\color{blue}{ 10 }$.

$$ \begin{aligned} 5- \frac{15x}{10} & \xlongequal{\text{Step 1}} \frac{5}{\color{red}{1}} - \frac{15x}{10} = \frac{ 5 \cdot \color{blue}{ 10 }}{ 1 \cdot \color{blue}{ 10 }} - \frac{ 15x }{ 10 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 50 } }{ 10 } - \frac{ \color{purple}{ 15x } }{ 10 }=\frac{ \color{purple}{ -15x+50 } }{ 10 } \end{aligned} $$

Multiply $ \dfrac{-15x+50}{10} $ by $ x^2 $ to get $ \dfrac{ -15x^3+50x^2 }{ 10 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{-15x+50}{10} \cdot x^2 & \xlongequal{\text{Step 1}} \frac{-15x+50}{10} \cdot \frac{x^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( -15x+50 \right) \cdot x^2 }{ 10 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -15x^3+50x^2 }{ 10 } \end{aligned} $$