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# Binomial Theorem

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How do I solve this?

What is the constant term of the expansion of $$\left( 6x + \frac{3}{x} \right)^4$$?

Mar 5, 2022

#1
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The general term is $$\binom{4}{n}(6x)^{n}(\frac{3}{x})^{4-n}$$. For the 6x and 3/x terms to balance out, n must equal 2.

$$\binom{4}{2} (6x)^2 (\frac{3}{x})^2 = 6 \cdot 36x^2 \cdot \frac{9}{x^2} = \boxed{1944}.$$

Mar 5, 2022