2. Given that
$$\frac { 4 \left( x ^ { 2 } + 6 \right) } { ( 1 - 2 x ) ( 2 + x ) ^ { 2 } } \equiv \frac { A } { ( 1 - 2 x ) } + \frac { B } { ( 2 + x ) } + \frac { C } { ( 2 + x ) ^ { 2 } }$$
- find the values of the constants \(A\) and \(C\) and show that \(B = 0\)
(4) - Hence, or otherwise, find the series expansion of
$$\frac { 4 \left( x ^ { 2 } + 6 \right) } { ( 1 - 2 x ) ( 2 + x ) ^ { 2 } } , \quad | x | < \frac { 1 } { 2 }$$
in ascending powers of \(x\), up to and including the term in \(x ^ { 2 }\), simplifying each term.
(5)