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# HALP!!!

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What is the constant term of the expansion of $$\left(6x+\dfrac{1}{3x}\right)^6$$?

May 18, 2020

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What's the constant term of the expansion of (do + not + cheat + on + your) * (A*o*P*S + Homework) ?

May 18, 2020
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Let up Hugo,

this is a standard maths question that could have come from any school or text book anywhere in the world.

Melody  May 19, 2020
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Hi Melody, while this may appear to be one, I perfectly recall this from being in... the lesson about "simon's favorite factoring trick" or +/- one lesson.

However I do understand that there are similar questions not property of AoPS and if I hadn't taken that particular course I would have thought it wasn't one, but I do remember having trouble with this one.

hugomimihu  May 19, 2020
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So what?

Students all over the whole world have been having trouble with this one for over a hundred years.

It is a completely standard question.

I do not even know why this is an AoPS question at all.  It is not problem-solving, it is a standard algebraic question.

Melody  May 19, 2020
edited by Melody  May 19, 2020
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$$\left(6x+\dfrac{1}{3x}\right)^6\\~\\ T_n=\begin{pmatrix} 6\\ n \end{pmatrix} (\frac{1}{3x})^n(6x)^{n-6}\\ \text{If you pull out the x terms you get } (\frac{1}{x})^n*x^{n-6} \\ \text{The constant term will have }x^0\qquad\\ \text{So solve for n}\\ etc$$