2. Find the 3rd term of (x + 2) ^ 8.

A 448x^5

B 28x^6

C 112x^6

D 4x^6

C

Step-by-step explanation:

The general formula for the binomial expansion is

(n over k) * (x) ^ (n - k) * y^k

n = 8

k = 2 which is the third term. That's because k starts at 0.

n over k = n C k = 8 C 2 = 8! / (8-2) ! * 2!

2^2 = 4

n over k = 8! / (6!) (2!) = 8*7 / 2 = 28

x^ (n - k) = x^ (8 - 2) = x ^6

So the result is

x^6 * 28 * 2^2

112 x^6

The answer is C