Edexcel C12 2017 June — Question 10

Exam BoardEdexcel
ModuleC12 (Core Mathematics 1 & 2)
Year2017
SessionJune
TopicBinomial Theorem (positive integer n)
TypeTwo equations from coefficients

  1. (a) Find the first 3 terms, in ascending powers of \(x\), of the binomial expansion of
$$\left( 2 - \frac { x } { 8 } \right) ^ { 10 }$$ giving each term in its simplest form. $$\mathrm { f } ( x ) = \left( 2 - \frac { x } { 8 } \right) ^ { 10 } ( a + b x ) , \text { where } a \text { and } b \text { are constants }$$ Given that the first two terms, in ascending powers of \(x\) in the series expansion of \(\mathrm { f } ( x )\), are 256 and \(352 x\),
(b) find the value of \(a\),
(c) find the value of \(b\).