Evaluate
\[ \left(2x – \frac{1}{x}\right)^2 \]
Solution:
Using identity:
\[ (a-b)^2 = a^2 – 2ab + b^2 \]
\[ \left(2x – \frac{1}{x}\right)^2 = (2x)^2 – 2\left(2x\right)\left(\frac{1}{x}\right) + \left(\frac{1}{x}\right)^2 \]
\[ = 4x^2 – 4 + \frac{1}{x^2} \]