Find the binomial expansion of \(( 1 + x ) ^ { - \frac { 1 } { 3 } }\) up to and including the term in \(x ^ { 2 }\).
(2 marks)
Hence find the binomial expansion of \(\left( 1 + \frac { 3 } { 4 } x \right) ^ { - \frac { 1 } { 3 } }\) up to and including the term in \(x ^ { 2 }\).
Hence show that \(\sqrt [ 3 ] { \frac { 256 } { 4 + 3 x } } \approx a + b x + c x ^ { 2 }\) for small values of \(x\), stating the values of the constants \(a , b\) and \(c\).