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)  = 2(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 )  = 1 + nax + [n(n-1) ax2] / 2! + [n(n-1)(n-2) a3 x3] / 3!

2(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)x/ 3!

= 32 { 1 + 2.5x + 2.5x2 + 1.25x3 }

= 32 + 80x + 80x2 + 40x3

Answered by Fiona O. Maths tutor

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