Question

Write the following square of binomial as trinomial:  \[\left( 3x - \frac{1}{3x} \right)^2\]

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.

\[\left( 3x - \frac{1}{3x} \right)^2 \]

\[ = \left( 3x \right)^2 - 2\left( 3x \right)\left( \frac{1}{3x} \right) + \left( \frac{1}{3x} \right)^2 \]

\[ = 9 x^2 - 2 + \frac{1}{9 x^2}\]