Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 2.3 Junior Find the answer

When simplified, the third term in the expansion of $(\frac{a}{\sqrt{x}}-\frac{\sqrt{x}}{a^2})^6$ is:

Pick one

Solution

By the Binomial Theorem, the third term in the expansion is
$\binom{6}{2}(\frac{a}{\sqrt{x}})^{4}(\frac{-\sqrt{x}}{a^2})^2$
$15 \cdot \frac{a^4}{x^2} \cdot \frac{x}{a^4}$
$\frac{15}{x}$
The answer is $\boxed{\textbf{(A)}}$ .

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