Obtain the binomial expansion of \(( 1 - x ) ^ { - 3 }\) up to and including the term in \(x ^ { 2 }\).
Hence obtain the binomial expansion of \(\left( 1 - \frac { 5 } { 2 } x \right) ^ { - 3 }\) up to and including the term in \(x ^ { 2 }\).
Find the range of values of \(x\) for which the binomial expansion of \(\left( 1 - \frac { 5 } { 2 } x \right) ^ { - 3 }\) would be valid.
Given that \(x\) is small, show that \(\left( \frac { 4 } { 2 - 5 x } \right) ^ { 3 } \approx a + b x + c x ^ { 2 }\), where \(a , b\) and \(c\) are integers.