Question

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

A) 10C3(e⁷)(2f)³
B) 10C3(e⁷)(f³)
C) 10C4(e⁶)(2f)⁴
D) 10C4(e⁶)(f⁴)

Answer 1

The expression representing the fourth term in the binomial expansion of (e + 2f)^10 is 10C4(e^6)(2f)^4 (option D).

Step-by-step explanation:

The binomial expansion of (e + 2f)10 can be found using the formula:

(a + b)n = C(n, 0)anb0 + C(n, 1)an-1b1 + C(n, 2)an-2b2 + ... + C(n, k)an-kbk + ... + C(n, n)a0bn

where C(n, k) represents the binomial coefficient and is given by:

C(n, k) = n! / (k! * (n-k)!)

In this case, n = 10, a = e, b = 2f, and we are looking for the fourth term, so k = 4.

Substituting the values into the formula, we get:

C(10, 4)(e10-4)(2f)4

Simplifying further, this becomes:

10C4(e6)(2f)4

Therefore, the correct expression for the fourth term in the binomial expansion is 10C4(e6)(2f)4 (option D).