which expression represents the fourth term in the binomial expansion of (e + 2f)^10?\n10c3(e^7)(2f)^3\n10c3(…

Explanation:

Step1: Recall binomial - theorem formula

The general term in the binomial expansion of ((a + b)^n) is given by (T_{r + 1}={n}C{r}a^{n - r}b^{r}), where (n) is the power of the binomial, (r) is the term - number minus 1, ({n}C{r}=\frac{n!}{r!(n - r)!}), (a) and (b) are the two terms of the binomial.

Step2: Identify values of (n), (a), (b), and (r)

For ((e + 2f)^{10}), we have (n = 10), (a=e), (b = 2f). We want the fourth term, so (r+1 = 4), which means (r = 3).

Step3: Substitute values into the formula

Substitute (n = 10), (r = 3), (a = e), and (b = 2f) into the formula (T_{r + 1}={n}C{r}a^{n - r}b^{r}). We get (T_{4}={10}C{3}e^{10 - 3}(2f)^{3}={10}C{3}(e^{7})(2f)^{3}).

Answer:

({10}C{3}(e^{7})(2f)^{3}) (First option)