Question

Expand ${(y-\frac{1}{y})}^2$ using appropriate identity

Answer 1

Using the identity is $(a-b{)}^2=a^2+b^2-2ab$.

Given: ${(y-\frac{1}{y})}^2$ we apply the above identity By taking $a=y$ and $b=-\frac{1}{y}$

We get, ${(y-\frac{1}{y})}^2={\left(y\right)}^2+{\left(\frac{1}{y}\right)}^2-(2\times y\times \frac{1}{y})=y^2+\frac{1}{y^2}-2$

Hence, ${(y-\frac{1}{y})}^2=y^2-2+\frac{1}{y^2}$.