WAEC 2011 · Paper 2 · Q3

(a)
Write down the binomial expansion of $(2 - x)^5$ in ascending powers of $x$ .
(b)
Use your expansion in (a) to evaluate $(1.98)^5$ correct to four decimal places.

Worked solution (try it first)

Each term is $\binom5r 2^{5 - r}(-x)^r$ , with coefficients $1, 5, 10, 10, 5, 1$ .
$r = 0$ : $32$ .
$r = 1$ : $5 \times 16 \times (-x) = -80x$ .
$r = 2$ : $10 \times 8 \times x^2 = 80x^2$ .
$r = 3$ : $10 \times 4 \times (-x^3) = -40x^3$ .
$r = 4$ : $5 \times 2 \times x^4 = 10x^4$ .
$r = 5$ : $-x^5$ .
So $(2 - x)^5 = 32 - 80x + 80x^2 - 40x^3 + 10x^4 - x^5$ .