Find $ \left(2x-y\right)^2 $ using formula.

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

where $ A = \color{blue}{ 2x } $ and $ B = \color{red}{ y }$.

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

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

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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