Find the square of:

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

Using the formula,

[∵ (x + y)² = x² + 2xy + y²]

$\Big(5x +\dfrac{1}{5x}\Big)^2\\[1em] = (5x)^2 + 2 \times 5x \times \dfrac{1}{5x} + \Big(\dfrac{1}{5x}\Big)^2\\[1em] = 25x^2 + \dfrac{10x}{5x} + \dfrac{1}{25x^2}\\[1em] = 25x^2 + 2 + \dfrac{1}{25x^2}$

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