NECO 2023 · Paper 1 · Q18

Find the first 4 terms in the expansion of $(1 + 2x)^{15}$ .

Worked solution (try it first)

Each term is $\binom{15}{r}(2x)^r$ .
The coefficients needed are $\binom{15}{1} = 15$ , $\binom{15}{2} = 105$ and $\binom{15}{3} = 455$ .
$r = 1$ : $15 \times 2x = 30x$ .
$r = 2$ : $105 \times 4x^2 = 420x^2$ .
$r = 3$ : $455 \times 8x^3 = 3640x^3$ .
So the first four terms are $1 + 30x + 420x^2 + 3640x^3$ , option C.