Moderate -0.8 This is a straightforward application of the binomial expansion requiring students to factor out the constant (rewrite as 16·2^(-2)·(1+x/2)^(-2)), then apply the standard formula for negative integer powers. It's routine bookwork with clear steps, easier than average but not trivial since it requires recognizing the factoring technique and careful arithmetic with negative powers.
1 Expand \(\frac { 16 } { ( 2 + x ) ^ { 2 } }\) in ascending powers of \(x\), up to and including the term in \(x ^ { 2 }\), simplifying the coefficients.
1 Expand $\frac { 16 } { ( 2 + x ) ^ { 2 } }$ in ascending powers of $x$, up to and including the term in $x ^ { 2 }$, simplifying the coefficients.
\hfill \mbox{\textit{CAIE P3 2011 Q1 [4]}}