Find the first four terms in the binomial expansion of (2 + x) ^5

Firstly we must take the 2 out of the bracket, as a binomial expansion must have a coefficent of 1

(2 + x) ⁵  = 2⁵ (1 + 0.5x) ⁵

Then, it is a good idea to quote the binomial expasion formula (you can often pick up extra marks for quoting formulae, even if your final answer is incorrect)

( x + a ) ⁿ  = 1 + nax + [n(n-1) a² x²] / 2! + [n(n-1)(n-2) a³ x³] / 3!

2⁵ (1 + 0.5x) ⁵ = 2⁵ { 1 + (5 x 0.5)x + (5 x 4 x 0.5²)x² / 2! + (5 x 4 x 3 x 0.5³)x³ / 3!

= 32 { 1 + 2.5x + 2.5x² + 1.25x³ }

= 32 + 80x + 80x² + 40x³