When simplified, the third term in the expansion of (a√x-√xa^2)^6 is:

1961 AMC 12 Problem 7

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When simplified, the third term in the expansion of

\left(\frac{a}{\sqrt{x}}-\frac{\sqrt{x}}{a^2}\right)^6

is:

\dfrac{15}{x}

-\dfrac{15}{x}

-\dfrac{6x^2}{a^9}

\dfrac{20}{a^3}

-\dfrac{20}{a^3}

The third term uses two copies of the second binomial term

Use the coefficient

\binom62

and simplify the powers of

a

and

x

The third term is

\begin{aligned} &\binom62\left(\frac a{\sqrt x}\right)^4 \left(-\frac{\sqrt x}{a^2}\right)^2\\ &\qquad=15\cdot\frac{a^4}{x^2}\cdot\frac{x}{a^4} =\frac{15}{x}. \end{aligned}

Therefore, the correct answer is A.