Multiply :

2x + $\dfrac{1}{2}$ y and 2x - $\dfrac{1}{2}$ y

$\Big(2x + \dfrac{1}{2}y\Big) \times \Big(2x - \dfrac{1}{2}y\Big)\\[1em] = 2x \times \Big(2x - \dfrac{1}{2}y\Big) + \dfrac{1}{2}y \times \Big(2x - \dfrac{1}{2}y\Big)\\[1em] =\Big(2x \times 2x - 2x \times \dfrac{1}{2}y\Big) + \Big(\dfrac{1}{2}y \times 2x - \dfrac{1}{2}y \times \dfrac{1}{2}y\Big)\\[1em] =\Big(4x^{1+1} - \dfrac{2xy}{2}\Big) + \Big(\dfrac{2xy}{2} - \dfrac{1 \times 1}{2 \times 2}y^{1+1}\Big)\\[1em] = (4x^2 - xy) + \Big(xy - \dfrac{1}{4}y^{2}\Big)\\[1em] = 4x^2 - xy + xy - \dfrac{1}{4}y^{2}\\[1em] = 4x^2 - \cancel{xy} + \cancel{xy} - \dfrac{1}{4}y^{2}\\[1em] = 4x^2 - \dfrac{1}{4}y^2$

Hence, 2x + $\dfrac{1}{2}$ y x 2x - $\dfrac{1}{2}$ y = 4x² - $\dfrac{1}{4}$ y²