Christopher S. answered • 07/12/19
Professionally Trained Math and Physics Tutor
This is a binomial distribution problem (a + b)^3 = a^3 + 3!/2!1! * a^2 * b^1 + ...
therefore we only need to identify what terms will have x^2 in them and then determine the coefficient from the factorials.
The complication is that we will be multiplying x and 1/x, so which powers will give us x^2? 4 and 2 will give us this outcome (note that it must be x^4 * (-1/x) ^2, the other way around will give us 1/x^2). Since we have even powers the negative will cancel out, so the term we are looking at is:
6!/4!2! * x^4 * (-1/x)^2 = 6!/4!2! * x^2
Hope this helps. I recommend looking up the binomial distribution (wikipedia is probably good) to get a better feel for how to calculate expansions using it. the ! symbol represents the factorial (i.e. 3! = 3*2*1). Let me know if anything is unclear. Note that you will have to reduce that coefficient to get the final answer, I have only provided the steps not the solution.
Christopher S.
Small error in the above. the x^4 term should include the 3, so the term should look like 6!/4!2! * (3x)^4 * (-1/x)^2 = 3^4 * 6!/4!2! * x^207/12/19