Multiply $20$ by $ \dfrac{x^2}{72} $ to get $ \dfrac{ 20x^2 }{ 72 } $.

Step 1: Write $ 20 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 20 \cdot \frac{x^2}{72} & \xlongequal{\text{Step 1}} \frac{20}{\color{red}{1}} \cdot \frac{x^2}{72} \xlongequal{\text{Step 2}} \frac{ 20 \cdot x^2 }{ 1 \cdot 72 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 20x^2 }{ 72 } \end{aligned} $$

Multiply $18$ by $ \dfrac{x^3}{2} $ to get $ \dfrac{ 18x^3 }{ 2 } $.

Step 1: Write $ 18 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 18 \cdot \frac{x^3}{2} & \xlongequal{\text{Step 1}} \frac{18}{\color{red}{1}} \cdot \frac{x^3}{2} \xlongequal{\text{Step 2}} \frac{ 18 \cdot x^3 }{ 1 \cdot 2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 18x^3 }{ 2 } \end{aligned} $$

Multiply $ \dfrac{20x^2}{72} $ by $ x $ to get $ \dfrac{ 20x^3 }{ 72 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{20x^2}{72} \cdot x & \xlongequal{\text{Step 1}} \frac{20x^2}{72} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 20x^2 \cdot x }{ 72 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 20x^3 }{ 72 } \end{aligned} $$

Multiply $ \dfrac{18x^3}{2} $ by $ x $ to get $ \dfrac{ 18x^4 }{ 2 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{18x^3}{2} \cdot x & \xlongequal{\text{Step 1}} \frac{18x^3}{2} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 18x^3 \cdot x }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 18x^4 }{ 2 } \end{aligned} $$

Multiply $ \dfrac{20x^2}{72} $ by $ x $ to get $ \dfrac{ 20x^3 }{ 72 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{20x^2}{72} \cdot x & \xlongequal{\text{Step 1}} \frac{20x^2}{72} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 20x^2 \cdot x }{ 72 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 20x^3 }{ 72 } \end{aligned} $$

Multiply $ \dfrac{18x^4}{2} $ by $ 2 $ to get $ 18x^4$.

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

Step 2: Cancel $ \color{red}{ 2 } $ in first and second fraction.

Step 3: Multiply numerators and denominators.

Step 4: Simplify numerator and denominator.

$$ \begin{aligned} \frac{18x^4}{2} \cdot 2 & \xlongequal{\text{Step 1}} \frac{18x^4}{2} \cdot \frac{2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{18x^4}{\color{red}{1}} \cdot \frac{\color{red}{1}}{1} = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 18x^4 \cdot 1 }{ 1 \cdot 1 } \xlongequal{\text{Step 4}} \frac{ 18x^4 }{ 1 } =18x^4 \end{aligned} $$

Add $ \dfrac{20x^3}{72} $ and $ 18x^4 $ to get $ \dfrac{ \color{purple}{ 1296x^4+20x^3 } }{ 72 }$.

Step 1: Write $ 18x^4 $ 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 $\color{blue}{72}$.

$$ \begin{aligned} \frac{20x^3}{72} +18x^4 & \xlongequal{\text{Step 1}} \frac{20x^3}{72} + \frac{18x^4}{\color{red}{1}} = \frac{ 20x^3 }{ 72 } + \frac{ 18x^4 \cdot \color{blue}{ 72 }}{ 1 \cdot \color{blue}{ 72 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 20x^3 } }{ 72 } + \frac{ \color{purple}{ 1296x^4 } }{ 72 }=\frac{ \color{purple}{ 1296x^4+20x^3 } }{ 72 } \end{aligned} $$