Find $ \left(x+2\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}{ 2 }$.

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

Multiply $ \dfrac{1}{2} $ by $ x^2+4x+4 $ to get $ \dfrac{ x^2+4x+4 }{ 2 } $.

Step 1: Write $ x^2+4x+4 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Multiply $ \dfrac{x^2+4x+4}{2} $ by $ x-5 $ to get $ \dfrac{x^3-x^2-16x-20}{2} $.

Step 1: Write $ x-5 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{x^2+4x+4}{2} \cdot x-5 & \xlongequal{\text{Step 1}} \frac{x^2+4x+4}{2} \cdot \frac{x-5}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( x^2+4x+4 \right) \cdot \left( x-5 \right) }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x^3-5x^2+4x^2-20x+4x-20 }{ 2 } = \frac{x^3-x^2-16x-20}{2} \end{aligned} $$