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Question
Write the following square of binomial as trinomial: \[\left( 3x - \frac{1}{3x} \right)^2\]
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Solution
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.
\[\left( 3x - \frac{1}{3x} \right)^2 \]
\[ = \left( 3x \right)^2 - 2\left( 3x \right)\left( \frac{1}{3x} \right) + \left( \frac{1}{3x} \right)^2 \]
\[ = 9 x^2 - 2 + \frac{1}{9 x^2}\]
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