Answer:
[tex]\large\boxed{\left(\dfrac{x}{2}-\dfrac{y}{2}\right)\left(\dfrac{x}{2}+\dfrac{y}{2}\right)=\dfrac{x-y}{2}\cdot\dfrac{x+y}{2}}[/tex]
Step-by-step explanation:
[tex]\dfrac{x^2}{4}-\dfrac{y^2}{4}=\dfrac{x^2}{2^2}-\dfrac{y^2}{2^2}\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\=\left(\dfrac{x}{2}\right)^2-\left(\dfrac{y}{2}\right)^2\qquad\text{use}\ (a-b)(a+b)=a^2-b^2\\\\=\left(\dfrac{x}{2}-\dfrac{y}{2}\right)\left(\dfrac{x}{2}+\dfrac{y}{2}\right)=\dfrac{x-y}{2}\cdot\dfrac{x+y}{2}[/tex]
