Find the square of:

$\dfrac{5a}{6b} -\dfrac{6b}{5a}$

Using the formula,

[∵ (x - y)² = x² - 2xy + y²]

$\Big(\dfrac{5a}{6b} - \dfrac{6b}{5a}\Big)^2\\[1em] = \Big(\dfrac{5a}{6b}\Big)^2 - 2 \times \dfrac{5a}{6b} \times \dfrac{6b}{5a} + \Big(\dfrac{6b}{5a}\Big)^2\\[1em] = \dfrac{25a^2}{36b^2} - \dfrac{2 \times 5a \times 6b}{6b \times 5a} + \dfrac{36b^2}{25a^2}\\[1em] = \dfrac{25a^2}{36b^2} - \dfrac{60ab}{30ab} + \dfrac{36b^2}{25a^2}\\[1em] = \dfrac{25a^2}{36b^2} - 2 + \dfrac{36b^2}{25a^2}$

Hence, $\Big(\dfrac{5a}{6b} - \dfrac{6b}{5a}\Big)^2 = \dfrac{25a^2}{36b^2} - 2 + \dfrac{36b^2}{25a^2}$