Question

Using a suitable identity, find the following product:

$(a-\frac{1}{a})(a-\frac{1}{a})$

Answer 1

using $(a-b)(a-b)=a^2+b^2-2ab$

For the above expression, keeping $a$ as $a$ and $b=\frac{1}{a}$, we get

$(a-\frac{1}{a})(a-\frac{1}{a})=(a^2-\frac{1}{a^2}-2)$