Multiply $48$ by $ \dfrac{p}{42} $ to get $ \dfrac{ 48p }{ 42 } $.

Step 1: Write $ 48 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 48 \cdot \frac{p}{42} & \xlongequal{\text{Step 1}} \frac{48}{\color{red}{1}} \cdot \frac{p}{42} \xlongequal{\text{Step 2}} \frac{ 48 \cdot p }{ 1 \cdot 42 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 48p }{ 42 } \end{aligned} $$

Multiply $ \dfrac{48p}{42} $ by $ p $ to get $ \dfrac{ 48p^2 }{ 42 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{48p}{42} \cdot p & \xlongequal{\text{Step 1}} \frac{48p}{42} \cdot \frac{p}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 48p \cdot p }{ 42 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 48p^2 }{ 42 } \end{aligned} $$

Add $ \dfrac{48p^2}{42} $ and $ 36 $ to get $ \dfrac{ \color{purple}{ 48p^2+1512 } }{ 42 }$.

Step 1: Write $ 36 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{42}$.

$$ \begin{aligned} \frac{48p^2}{42} +36 & \xlongequal{\text{Step 1}} \frac{48p^2}{42} + \frac{36}{\color{red}{1}} = \frac{ 48p^2 }{ 42 } + \frac{ 36 \cdot \color{blue}{ 42 }}{ 1 \cdot \color{blue}{ 42 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 48p^2 } }{ 42 } + \frac{ \color{purple}{ 1512 } }{ 42 }=\frac{ \color{purple}{ 48p^2+1512 } }{ 42 } \end{aligned} $$