Question

Write the following square of binomial as trinomial:  \[\left( \frac{x}{y} - \frac{y}{x} \right)^2\]

Answer 1

 We will use the identities

\[\left( a + b \right)^2 = a^2 + 2ab + b^2 \text { and } \left( a - b \right)^2 = a^2 - 2ab + b^2\] to convert the squares of binomials as trinomials.

\[ \left( \frac{x}{y} - \frac{y}{x} \right)^2 \]

\[ = \left( \frac{x}{y} \right)^2 - 2\left( \frac{x}{y} \right)\left( \frac{y}{x} \right) + \left( \frac{y}{x} \right)^2 \]

\[ = \frac{x^2}{y^2} - 2 + \frac{y^2}{x^2}\]