Multiply $7$ by $ \dfrac{n}{4} $ to get $ \dfrac{ 7n }{ 4 } $.

Step 1: Write $ 7 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 7 \cdot \frac{n}{4} & \xlongequal{\text{Step 1}} \frac{7}{\color{red}{1}} \cdot \frac{n}{4} \xlongequal{\text{Step 2}} \frac{ 7 \cdot n }{ 1 \cdot 4 } \xlongequal{\text{Step 3}} \frac{ 7n }{ 4 } \end{aligned} $$

Multiply $ \dfrac{7n}{4} $ by $ n^2 $ to get $ \dfrac{ 7n^3 }{ 4 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{7n}{4} \cdot n^2 & \xlongequal{\text{Step 1}} \frac{7n}{4} \cdot \frac{n^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 7n \cdot n^2 }{ 4 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 7n^3 }{ 4 } \end{aligned} $$

Add $n^2$ and $ \dfrac{7n^3}{4} $ to get $ \dfrac{ \color{purple}{ 7n^3+4n^2 } }{ 4 }$.

Step 1: Write $ n^2 $ 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 first fraction by $\color{blue}{ 4 }$.

$$ \begin{aligned} n^2+ \frac{7n^3}{4} & \xlongequal{\text{Step 1}} \frac{n^2}{\color{red}{1}} + \frac{7n^3}{4} = \frac{ n^2 \cdot \color{blue}{ 4 }}{ 1 \cdot \color{blue}{ 4 }} + \frac{ 7n^3 }{ 4 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 4n^2 } }{ 4 } + \frac{ \color{purple}{ 7n^3 } }{ 4 }=\frac{ \color{purple}{ 7n^3+4n^2 } }{ 4 } \end{aligned} $$

Add $ \dfrac{7n^3+4n^2}{4} $ and $ 28n $ to get $ \dfrac{ \color{purple}{ 7n^3+4n^2+112n } }{ 4 }$.

Step 1: Write $ 28n $ 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 $\color{blue}{4}$.

$$ \begin{aligned} \frac{7n^3+4n^2}{4} +28n & \xlongequal{\text{Step 1}} \frac{7n^3+4n^2}{4} + \frac{28n}{\color{red}{1}} = \frac{ 7n^3+4n^2 }{ 4 } + \frac{ 28n \cdot \color{blue}{ 4 }}{ 1 \cdot \color{blue}{ 4 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 7n^3+4n^2 } }{ 4 } + \frac{ \color{purple}{ 112n } }{ 4 }=\frac{ \color{purple}{ 7n^3+4n^2+112n } }{ 4 } \end{aligned} $$