Question

Factorize each of the following expression:

\[\frac{50}{x^2} - \frac{2 x^2}{81}\]

Answer 1

\[\frac{50}{x^2} - \frac{2 x^2}{81}\]
\[ = 2\left( \frac{25}{x^2} - \frac{x^2}{81} \right)\]
\[ = 2\left\{ \left( \frac{5}{x} \right)^2 - \left( \frac{x}{9} \right)^2 \right\}\]
\[ = 2\left( \frac{5}{x} - \frac{x}{9} \right)\left( \frac{5}{x} + \frac{x}{9} \right)\]