Question 2 - A-Level Maths

Exam Board	Edexcel
Module	P2 (Pure Mathematics 2)
Year	2020
Session	January
Topic	Binomial Theorem (positive integer n)
Type	Product with unknown constant to determine

2. One of the terms in the binomial expansion of $( 3 + a x ) ^ { 6 }$, where $a$ is a constant, is $540 x ^ { 4 }$

Find the possible values of $a$.
Hence find the term independent of $x$ in the expansion of $$\left( \frac { 1 } { 81 } + \frac { 1 } { x ^ { 6 } } \right) ( 3 + a x ) ^ { 6 }$$