Moderate -0.3 This is a straightforward application of the binomial expansion for fractional powers with a simple coefficient (4x), requiring routine substitution into the formula and basic arithmetic to simplify coefficients. The validity condition is standard recall. Slightly easier than average due to being a direct textbook-style question with no problem-solving element.
2. (i) Expand \(( 1 + 4 x ) ^ { \frac { 3 } { 2 } }\) 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) Expand $( 1 + 4 x ) ^ { \frac { 3 } { 2 } }$ 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 [5]}}