2.
$$f ( x ) = ( 125 - 5 x ) ^ { \frac { 2 } { 3 } } \quad | x | < 25$$
- Find the binomial expansion of \(\mathrm { f } ( x )\), in ascending powers of \(x\), up to and including the term in \(x ^ { 2 }\), giving the coefficient of \(x\) and the coefficient of \(x ^ { 2 }\) as simplified fractions.
- Use your expansion to find an approximate value for \(120 ^ { \frac { 2 } { 3 } }\), stating the value of \(x\) which you have used and showing your working. Give your answer to 5 decimal places.