Edexcel A-Level Mathematics AS P2.4.5 Binomial Expansion for Positive Integer Powers Questions

Practise expanding positive integer powers, finding coefficients and using early binomial terms for algebraic constants or approximations.

Exam points

expand (a+bx)^n in ascending powers, simplifying coefficients with nCr
find a specified coefficient or unknown constant by matching powers of x

[Maximum number: 3]

A curve C has equation y=f(x) where

f(x)=(2-k x)^{5}

and k is a constant.
Given that when f(x) is divided by (4 x-5) the remainder is $\frac{243}{32}$

Find the first three terms, in ascending powers of x, of the binomial expansion of

\left(2-\frac{2}{5} x\right)^{5}

giving each term in simplest form.

Using the solution to part (b) and making your method clear,

$\pm^{5} C_{1} \times 2^{4} \times\left( \pm \frac{2}{5} x\right)$ or $\pm{ }^{5} C_{2} \times 2^{3} \times\left( \pm \frac{2}{5} x\right)^{2}$ $32-32 x+\frac{64}{5} x^{2}$
(3)

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Edexcel A-Level Mathematics AS P2.4.5 Binomial Expansion for Positive Integer Powers Questions question 1