Which expression represents the fourth term in the binomial expansion of e^2f10?

To find the fourth term in the binomial expansion of the expression e^2f10, we start by recognizing that this expression can be rewritten as (2f)¹⁰. The binomial expansion can be applied using the general formula:

(a + b)ⁿ = Σ [C(n, k) * a^n-k * b^k], where C(n, k) is the binomial coefficient.

In our case, consider it as (-e and e) and we apply it to the exponent:

Expanding (a + b)¹⁰ for the fourth term (k=3), we get:

C(10, 3) * (2f)^10-3 * (e)³

Calculating C(10, 3):

C(10, 3) = 10! / (3!(10-3)!) = 120

Hence, the expression for the fourth term becomes:

120 * (2f)⁷ * e³

So, the fourth term in the binomial expansion of e^2f10 is:

120 * (2f)⁷ * e³