Question

Write the following square of binomial as trinomial:  \[\left( \frac{2a}{3b} + \frac{2b}{3a} \right)^2\]

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.

\[ \left( \frac{2a}{3b} + \frac{2b}{3a} \right)^2 \]

\[ = \left( \frac{2a}{3b} \right)^2 + 2$\left( \frac{2a}{3b} \right)$\left( \frac{2b}{3a} \right) + \left( \frac{2b}{3a} \right)^2 \]

\[ = \frac{4 a^2}{9 b^2} + \frac{8}{9} + \frac{4 b^2}{9 a^2}\]