Question

how do do a binomial expansion when x is in both terms

Answer 1

Do you have the problem?

Answer 2

find the coefficient of x in the expansion (2x+3/x)^6

Answer 3

Do you know
\[\Large ^nC_r(q)^r(p)^{n-r}\]
Where
\((p+q)^n\)

Answer 4

yes, but I dont understand when there is an x in both terms
oh and I'm trying to find the coefficient of x^3

Answer 5

The expanded form of that is
\[64 x^6+\frac{729}{x^6}+576 x^4+\frac{2916}{x^4}+2160 x^2+\frac{4860}{x^2}+4320\]

Answer 6

There's no x^3 term

Answer 7

It doesn't matter just consider them as two different terms and follow the formula. Also the first term has x and the second has 1/x , so when you expand it some of the x's get cancelled out.

Answer 8

You still can't get anything from there

Answer 9

ok thanks :)