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

Guest May 18, 2020

#1**0 **

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

hugomimihu May 18, 2020

#2**0 **

**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

#3**0 **

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

#5**+1 **

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

**Please no other answerer finish this. **

Melody May 19, 2020