Expand:

$\Big(a +\dfrac{1}{2a}\Big)^2$

$\Big(a +\dfrac{1}{2a}\Big)^2$

Using the formula:

(∵ (x + y)² = x² + 2xy + y²)

$= (a)^2 + 2 \times a \times \dfrac{1}{2a} + \Big(\dfrac{1}{2a}\Big)^2\\[1em] = a^2 + \dfrac{2a}{2a} + \dfrac{1}{4a^2}\\[1em] = a^2 + 1 + \dfrac{1}{4a^2}$

Hence, $\Big(a +\dfrac{1}{2a}\Big)^2$ = $a^2 + 1 + \Big(\dfrac{1}{4a^2}\Big)$