Question

Write the following square of binomial as trinomial:  \[\left( 9a + \frac{1}{6} \right)^2\]

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.

\[ \left( 9a + \frac{1}{6} \right)^2 \]

\[ = \left( 9a \right)^2 + 2\left( 9a \right)\left( \frac{1}{6} \right) + \left( \frac{1}{6} \right)^2 \]

\[ = 81 a^2 + 3a + \frac{1}{36}\]