AQA C2 2013 January — Question 8

Exam BoardAQA
ModuleC2 (Core Mathematics 2)
Year2013
SessionJanuary
TopicBinomial Theorem (positive integer n)
TypeProduct with reciprocal term binomial

8
  1. Expand \(\left( 1 + \frac { 4 } { x } \right) ^ { 2 }\).
  2. The first four terms of the binomial expansion of \(\left( 1 + \frac { x } { 4 } \right) ^ { 8 }\) in ascending powers of \(x\) are \(1 + a x + b x ^ { 2 } + c x ^ { 3 }\). Find the values of the constants \(a , b\) and \(c\).
  3. Hence find the coefficient of \(x\) in the expansion of \(\left( 1 + \frac { 4 } { x } \right) ^ { 2 } \left( 1 + \frac { x } { 4 } \right) ^ { 8 }\).