Find $ \left(x+4\right)^2 $ using formula.

$$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$

where $ A = \color{blue}{ x } $ and $ B = \color{red}{ 4 }$.

$$ \begin{aligned}\left(x+4\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot 4 + \color{red}{4^2} = x^2+8x+16\end{aligned} $$

Multiply $ \dfrac{1}{2} $ by $ x^2+8x+16 $ to get $ \dfrac{ x^2+8x+16 }{ 2 } $.

Step 1: Write $ x^2+8x+16 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{1}{2} \cdot x^2+8x+16 & \xlongequal{\text{Step 1}} \frac{1}{2} \cdot \frac{x^2+8x+16}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 1 \cdot \left( x^2+8x+16 \right) }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x^2+8x+16 }{ 2 } \end{aligned} $$

Add $ \dfrac{x^2+8x+16}{2} $ and $ 6 $ to get $ \dfrac{ \color{purple}{ x^2+8x+28 } }{ 2 }$.

Step 1: Write $ 6 $ 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 $\color{blue}{2}$.

$$ \begin{aligned} \frac{x^2+8x+16}{2} +6 & \xlongequal{\text{Step 1}} \frac{x^2+8x+16}{2} + \frac{6}{\color{red}{1}} = \frac{ x^2+8x+16 }{ 2 } + \frac{ 6 \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ x^2+8x+16 } }{ 2 } + \frac{ \color{purple}{ 12 } }{ 2 }=\frac{ \color{purple}{ x^2+8x+28 } }{ 2 } \end{aligned} $$