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
