Which expression represents the fourth term in the binomial expansion of (e + 2f)¹⁰?
¹⁰C₃(e⁷)(2f)^3
10C₃(e⁷)(f)^3
10C₄(e⁶)(2f)^4
10C₄(e⁶)(f)⁴

Solution:

Given, the expression is (e + 2f)¹⁰.

We have to find the fourth term in the binomial expansion of the given expression.

The general binomial expansion formula is given by

\((x+y)^{n}=^{n}C_{r}x^{(n-r)}y^{r}\)

Here, x = e, y = 2f, n = 10, r = 4

\((e+2f)^{10}=^{10}C_{4}(e)^{(10-4)}(2f)^{4}\)

\((e+2f)^{10}=^{10}C_{4}(e)^{(6)}(2f)^{4}\)

Therefore, the fourth term of the given binomial expression is \((e+2f)^{10}=^{10}C_{4}(e)^{(6)}(2f)^{4}\)

Which expression represents the fourth term in the binomial expansion of (e + 2f)¹⁰?

Summary:

The expression represents the sixth term in the binomial expansion of (e + 2f)¹⁰ is ¹⁰C₄(e⁶)(2f)⁴