Find the square of:

$a +\dfrac{1}{5a}$

$(a +\dfrac{1}{5a})^2$

Using the formula

(∵ (x + y)² = x² + 2xy + y²)

$= a^2 + 2 \times a \times \dfrac{1}{5a} + \dfrac{1}{5a}^2\\[1em] = a^2 + \dfrac{2a}{5a} + \dfrac{1}{25a^2}\\[1em] = a^2 + \dfrac{2}{5} + \dfrac{1}{25a^2}$

Hence, $(a +\dfrac{1}{5a})^2$ = a² + $\dfrac{2}{5}$ + $\dfrac{1}{25a^2}$