Moderate -0.8 This is a straightforward binomial theorem application requiring students to write out two coefficient terms, set them equal, and solve for k. The algebra is simple (single variable, linear after simplification) and the method is a standard textbook exercise with no conceptual challenges beyond basic binomial coefficient recall.
2 In the expansion of \(( x + 2 k ) ^ { 7 }\), where \(k\) is a non-zero constant, the coefficients of \(x ^ { 4 }\) and \(x ^ { 5 }\) are equal. Find the value of \(k\).
2 In the expansion of $( x + 2 k ) ^ { 7 }$, where $k$ is a non-zero constant, the coefficients of $x ^ { 4 }$ and $x ^ { 5 }$ are equal. Find the value of $k$.
\hfill \mbox{\textit{CAIE P1 2015 Q2 [4]}}