Find the coefficient of

Question

𝑥3
𝑖𝑛 𝑡ℎ𝑒 𝑒𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛 𝑜𝑓 1
1+𝑥
A. -1
B. -6
C. 1
D. 6

Answer 1

We can use the binomial theorem to expand the expression:

(1 + x)^1 = 1 + 1x

(1 + x)^2 = 1 + 2x + 1x^2

(1 + x)^3 = 1 + 3x + 3x^2 + 1x^3

So, the coefficient of 𝑥^3 in the expansion of (1 + 𝑥)^1 is 0, and the coefficient of 𝑥^3 in the expansion of (1 + 𝑥)^2 is also 0. The coefficient of 𝑥^3 in the expansion of (1 + 𝑥)^3 is 1. Therefore, the answer is:

C. 1