4. (a) Expand \(( 1 + a x ) ^ { - 3 } , | a x | < 1\), in ascending powers of \(x\) up to and including the term in \(x ^ { 3 }\). Give each coefficient as simply as possible in terms of the constant \(a\). Given that the coefficient of \(x ^ { 2 }\) in the expansion of \(\frac { 6 - x } { ( 1 + a x ) ^ { 3 } } , | a x | < 1\), is 3 ,
(b) find the two possible values of \(a\). Given also that \(a < 0\),
(c) show that the coefficient of \(x ^ { 3 }\) in the expansion of \(\frac { 6 - x } { ( 1 + a x ) ^ { 3 } }\) is \(\frac { 14 } { 9 }\).
4. continued