The expression \(( 1 - 2 x ) ^ { 4 }\) can be written in the form
$$1 + p x + q x ^ { 2 } - 32 x ^ { 3 } + 16 x ^ { 4 }$$
By using the binomial expansion, or otherwise, find the values of the integers \(p\) and \(q\).
Find the coefficient of \(x\) in the expansion of \(( 2 + x ) ^ { 9 }\).
Find the coefficient of \(x\) in the expansion of \(( 1 - 2 x ) ^ { 4 } ( 2 + x ) ^ { 9 }\).