Question 6 - A-Level Maths

Exam Board	CAIE
Module	P1 (Pure Mathematics 1)
Year	2010
Session	June
Topic	Binomial Theorem (positive integer n)
Type	Coefficient zero after multiplying binomial

Find the first 3 terms in the expansion of \(( 1 + a x ) ^ { 5 }\) in ascending powers of \(x\).
Given that there is no term in \(x\) in the expansion of \(( 1 - 2 x ) ( 1 + a x ) ^ { 5 }\), find the value of the constant \(a\).
For this value of \(a\), find the coefficient of \(x ^ { 2 }\) in the expansion of \(( 1 - 2 x ) ( 1 + a x ) ^ { 5 }\).