Edexcel IALGeneralGeneral Applications8 Marks

(a) Find the first 3 terms, in ascending powers of `x`, of the binomial expansion of `(2 - 9x)^4`. Give each term in its simplest form. (b) Using the answer to part (a), estimate the value of `(1.991)^4`.

(a)Find the first 3 terms, in ascending powers of `x`, of the binomial expansion of `(2 - 9x)^4`. Give each term in its simplest form.[5]
(b)Using the answer to part (a), estimate the value of `(1.991)^4`.[3]

Mark scheme

Marking points from the official mark scheme. The mark or mark type is shown in brackets.

M1 for an attempt at the binomial expansion `(2 ± 9x)⁴` with at least 3 terms. (Needs `(.)⁴ + 4(.)³(.) + 6(.)²(.)² + ...`).
A1 for `2^4` or `16`.
A1 for `4(2^3)(-9x)` or `-288x`.
A1 for `6(2^2)(-9x)^2` or `1944x^2`.
A1 for `16 - 288x + 1944x^2`.
M1 for setting `2 - 9x = 1.991` and finding `x`. (`9x = 0.009 \Rightarrow x = 0.001`).
M1 for substituting their `x` into their expansion from part (a).
A1 for `16 - 288(0.001) + 1944(0.001)^2 = 16 - 0.288 + 0.001944 = 15.713944`. (Accept `15.714`).

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