Multiply $ \color{blue}{x^2} $ by $ \left( 4-x\right) $ $$ \color{blue}{x^2} \cdot \left( 4-x\right) = 4x^2-x^3 $$

Find $ \left(4-x\right)^3 $ using formula

$$ (A - B) = A^3 - 3A^2B + 3AB^2 - B^3 $$

where $ A = 4 $ and $ B = x $.

$$ \left(4-x\right)^3 = 4^3-3 \cdot 4^2 \cdot x + 3 \cdot 4 \cdot x^2-x^3 = 64-48x+12x^2-x^3 $$

Add $4x^2-x^3$ and $ \dfrac{64-48x+12x^2-x^3}{3} $ to get $ \dfrac{ \color{purple}{ -4x^3+24x^2-48x+64 } }{ 3 }$.

Step 1: Write $ 4x^2-x^3 $ 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 $\color{blue}{ 3 }$.

$$ \begin{aligned} 4x^2-x^3+ \frac{64-48x+12x^2-x^3}{3} & \xlongequal{\text{Step 1}} \frac{4x^2-x^3}{\color{red}{1}} + \frac{64-48x+12x^2-x^3}{3} = \frac{ \left( 4x^2-x^3 \right) \cdot \color{blue}{ 3 }}{ 1 \cdot \color{blue}{ 3 }} + \frac{ 64-48x+12x^2-x^3 }{ 3 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 12x^2-3x^3 } }{ 3 } + \frac{ \color{purple}{ 64-48x+12x^2-x^3 } }{ 3 }=\frac{ \color{purple}{ -4x^3+24x^2-48x+64 } }{ 3 } \end{aligned} $$

Add $ \dfrac{-4x^3+24x^2-48x+64}{3} $ and $ 4-x $ to get $ \dfrac{ \color{purple}{ -4x^3+24x^2-51x+76 } }{ 3 }$.

Step 1: Write $ 4-x $ 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 $\color{blue}{3}$.

$$ \begin{aligned} \frac{-4x^3+24x^2-48x+64}{3} +4-x & \xlongequal{\text{Step 1}} \frac{-4x^3+24x^2-48x+64}{3} + \frac{4-x}{\color{red}{1}} = \frac{ -4x^3+24x^2-48x+64 }{ 3 } + \frac{ \left( 4-x \right) \cdot \color{blue}{ 3 }}{ 1 \cdot \color{blue}{ 3 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -4x^3+24x^2-48x+64 } }{ 3 } + \frac{ \color{purple}{ 12-3x } }{ 3 }=\frac{ \color{purple}{ -4x^3+24x^2-51x+76 } }{ 3 } \end{aligned} $$