Question

What is the fourth term of the expansion of the binomial (2x + 5)5? A. 10x2 B. 5,000x2 C. 1,250x3 D. 2,000x3

Answer 1

B would be the answer for this question.

Explanation:

Answer 2

Answer: The fourth term is
`5000x^2.`

Step-by-step explanation: We are given to find the fourth term in the expansion of the following binomial :

`B=(2x+5)^5.`

We know that

the r-th term in the expansion of the binomial
`(a+x)^n` is given by

`T_r=^nC_ra^(n-(r-1))b^(r-1).`

For the given term, we have

n = 5 and r = 4.

Therefore, fourth term is given by

`T_4\\\\=^5C_(4-1)(2x)^(5-(4-1))5^(4-1)\\\\=^5C_3(2x)^25^3\\\\=(5!)/(3!(5-3)!)*4x^2*125\\\\\\=(5*4)/(2*1)* 500x^2\\\\=5000x^2.`

Thus, the fourth term is
`5000x^2.`