Question

2. Find the 3rd term of(x + 2)^ 8.
A 448x^5
B 28x^6
C 112x^6
D 4x^6

Answer 1

C

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