CAIE P3 2009 June — Question 5

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2009
SessionJune
TopicGeneralised Binomial Theorem
TypeFinding unknown constant from coefficient

5 When \(( 1 + 2 x ) ( 1 + a x ) ^ { \frac { 2 } { 3 } }\), where \(a\) is a constant, is expanded in ascending powers of \(x\), the coefficient of the term in \(x\) is zero.
  1. Find the value of \(a\).
  2. When \(a\) has this value, find the term in \(x ^ { 3 }\) in the expansion of \(( 1 + 2 x ) ( 1 + a x ) ^ { \frac { 2 } { 3 } }\), simplifying the coefficient.