Moderate -0.3 This is a straightforward application of the binomial expansion formula for negative indices with routine algebraic simplification. While it requires careful handling of coefficients and knowledge of validity conditions (|3x/2| < 1), it's a standard C4 textbook exercise with no problem-solving or novel insight required, making it slightly easier than average.
2. (i) Find the binomial expansion of \(( 2 - 3 x ) ^ { - 3 }\) in ascending powers of \(x\) up to and including the term in \(x ^ { 3 }\), simplifying each coefficient.
(ii) State the set of values of \(x\) for which your expansion is valid.
2. (i) Find the binomial expansion of $( 2 - 3 x ) ^ { - 3 }$ in ascending powers of $x$ up to and including the term in $x ^ { 3 }$, simplifying each coefficient.\\
(ii) State the set of values of $x$ for which your expansion is valid.\\
\hfill \mbox{\textit{OCR C4 Q2 [6]}}