Question 3 - A-Level Maths

Exam Board	CAIE
Module	P1 (Pure Mathematics 1)
Year	2024
Session	June
Topic	Binomial Theorem (positive integer n)
Type	Product with unknown constant to determine

3 The coefficient of \(x ^ { 3 }\) in the expansion of \(( 3 + \mathrm { ax } ) ^ { 6 }\) is 160 .

Find the value of the constant \(a\).
Hence find the coefficient of \(x ^ { 3 }\) in the expansion of \(( 3 + \mathrm { ax } ) ^ { 6 } ( 1 - 2 \mathrm { x } )\).