Question

(a) Find the first 3 terms, in ascending powers of x, of the binomial expansion of

(2+kx)²
where k is a constant. Give each term in its simplest form.

Given that the coefficient of x is 6 times the coefficient of x,
(b) find the value of k.

Answer 1

3/2

Explanation:

(a) The first three terms, in ascending powers of x, of the binomial expansion of (2 + kx)² are:

(2 + kx)² = 2² = 4

(2 + kx)² = 2 * 2 * kx = 4kx

(2 + kx)² = 2 * k² x² = 4k² x²

(b) If the coefficient of x is 6 times the coefficient of x, then 6 = 4k. Therefore, k = 6/4 = 3/2.