What is the fourth term of the expansion of the binomial (2x+5)^5?

answer options:

a) 10x^2
b) 5,000x^2
c) 1,250x^3
d) 2,000x^3

B) 5000x^2

Step-by-step explanation:

The exponent of x starts at 5 in the first term and decreases by 1 as the term numbers increase by 1. Hence, the 4th term will have 2 as the exponent of x. (It will have 5-2=3 as the exponent of 5.)

Pascal's triangle tells you the coefficients of the 6 terms in the expansion will be 1, 5, 10, 10, 5, 1, so the 4th term has a coefficient of 10.

The 4th term will be ...

10(2x)^2(5)^3 = 10·4·125·x^2 = 5000x^2