- (a) Use the binomial series to find the expansion of
$$\frac { 1 } { ( 2 + 3 x ) ^ { 3 } } \quad | x | < \frac { 2 } { 3 }$$
in ascending powers of \(x\), up to and including the term in \(x ^ { 2 }\), giving each term as a simplified fraction.
(b) Hence or otherwise, find the coefficient of \(x ^ { 2 }\) in the series expansion of
- \(\frac { 1 } { ( 2 + 6 x ) ^ { 3 } } \quad | x | < \frac { 1 } { 3 }\)
- \(\frac { 4 - x } { ( 2 + 3 x ) ^ { 3 } } \quad | x | < \frac { 2 } { 3 }\)