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

Creeperhissboom
Apr 16, 2018

#1**+2 **

Well...let's see!!!

(6x + 1/ (3x) )^6 =

(6x)^6 + 6 * (6x)^5 (1/ (3x) ) + 15* (6x)^4 (1/(3x))^2 + 20* (6x)^3*(1 /(3x))^3

+ 15(6x)^2 * (1/(3x))^4 + 6* (6x)(1/(3x) )^5 + (1/ (3x))^6

The constant term is in red

20 * 216x^3 / (27x^3) = 20 *216 / 27 = 20 *24 / 3 = 20 * 8 = 160

CPhill
Apr 17, 2018

#2**+2 **

Hey Chris!

Just a quick question, if I do the problem, I will probably hard expand it, but is there are better way that just isolates the constant?

A way that doesn't require you to expand the whole expression?

GYanggg
Apr 17, 2018