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

Answer:

B would be the answer for this question.

Step-by-step 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

$T_4\\\\=^5C_{4-1}(2x)^{5-(4-1)}5^{4-1}\\\\=^5C_3(2x)^25^3\\\\=\dfrac{5!}{3!(5-3)!}\times4x^2\times125\\\\\\=\dfrac{5\times4}{2\times1}\times 500x^2\\\\=5000x^2.$

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