CAIE P1 2023 June — Question 3

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2023
SessionJune
TopicBinomial Theorem (positive integer n)
TypeCoefficient zero after multiplying binomial

3
  1. Give the complete expansion of \(\left( x + \frac { 2 } { x } \right) ^ { 5 }\).
  2. In the expansion of \(\left( a + b x ^ { 2 } \right) \left( x + \frac { 2 } { x } \right) ^ { 5 }\), the coefficient of \(x\) is zero and the coefficient of \(\frac { 1 } { x }\) is 80 . Find the values of the constants \(a\) and \(b\).