Question

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

a. 10C3(e7)(2f)3
b. 10C3(e7)(f)3
c. 10C4(e6)(2f)4
d. 10C4(e6)(f)4

Answer 1

A: 10C3(e7)(2f)3

Explanation:

Answer 2

The fourth term of the binomial expansion
`(e+2f)^(10)` can be calculated using the formula for (i+1)-th term of the binomial expansion:

`T_(i+1)=C_(10)^i\cdot e^(10-i)\cdot (2f)^i.`

In order to find term
`T_4`, determine that

`i+1=4\Rightarrow i=3.`

Now

`T_4=C_(10)^3\cdot e^(10-3)\cdot (2f)^3=C_(10)^3\cdot e^7\cdot (2f)^3.`

Answer: correct choice is A