Use the distributive property.

Multiply $36$ by $ \dfrac{x}{27} $ to get $ \dfrac{ 36x }{ 27 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 36 \cdot \frac{x}{27} & \xlongequal{\text{Step 1}} \frac{36}{\color{red}{1}} \cdot \frac{x}{27} \xlongequal{\text{Step 2}} \frac{ 36 \cdot x }{ 1 \cdot 27 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 36x }{ 27 } \end{aligned} $$

Subtract $ \dfrac{36x}{27} $ from $ 63 $ to get $ \dfrac{ \color{purple}{ -36x+1701 } }{ 27 }$.

Step 1: Write $ 63 $ 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 $\color{blue}{ 27 }$.

$$ \begin{aligned} 63- \frac{36x}{27} & \xlongequal{\text{Step 1}} \frac{63}{\color{red}{1}} - \frac{36x}{27} = \frac{ 63 \cdot \color{blue}{ 27 }}{ 1 \cdot \color{blue}{ 27 }} - \frac{ 36x }{ 27 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 1701 } }{ 27 } - \frac{ \color{purple}{ 36x } }{ 27 }=\frac{ \color{purple}{ -36x+1701 } }{ 27 } \end{aligned} $$

Multiply $ \dfrac{-36x+1701}{27} $ by $ x^2 $ to get $ \dfrac{ -36x^3+1701x^2 }{ 27 } $.

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.

$$ \begin{aligned} \frac{-36x+1701}{27} \cdot x^2 & \xlongequal{\text{Step 1}} \frac{-36x+1701}{27} \cdot \frac{x^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( -36x+1701 \right) \cdot x^2 }{ 27 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -36x^3+1701x^2 }{ 27 } \end{aligned} $$

Subtract $18x$ from $ \dfrac{-36x^3+1701x^2}{27} $ to get $ \dfrac{ \color{purple}{ -36x^3+1701x^2-486x } }{ 27 }$.

Step 1: Write $ 18x $ 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 $\color{blue}{27}$.

$$ \begin{aligned} \frac{-36x^3+1701x^2}{27} -18x & \xlongequal{\text{Step 1}} \frac{-36x^3+1701x^2}{27} - \frac{18x}{\color{red}{1}} = \frac{ -36x^3+1701x^2 }{ 27 } - \frac{ 18x \cdot \color{blue}{ 27 }}{ 1 \cdot \color{blue}{ 27 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -36x^3+1701x^2 } }{ 27 } - \frac{ \color{purple}{ 486x } }{ 27 }=\frac{ \color{purple}{ -36x^3+1701x^2-486x } }{ 27 } \end{aligned} $$