Moderate -0.3 This is a straightforward binomial expansion question requiring standard application of the formula to find terms, then solving a simple equation when coefficients are equal. The algebra is routine and the problem-solving demand is minimal, making it slightly easier than average but not trivial since it requires connecting multiple parts.
3. (a) Find the first four terms, in ascending powers of \(x\), in the binomial expansion of \(( 1 + k x ) ^ { 6 }\), where \(k\) is a non-zero constant.
Given that, in this expansion, the coefficients of \(x\) and \(x ^ { 2 }\) are equal, find
(b) the value of \(k\),
(c) the coefficient of \(x ^ { 3 }\).
3. (a) Find the first four terms, in ascending powers of $x$, in the binomial expansion of $( 1 + k x ) ^ { 6 }$, where $k$ is a non-zero constant.
Given that, in this expansion, the coefficients of $x$ and $x ^ { 2 }$ are equal, find\\
(b) the value of $k$,\\
(c) the coefficient of $x ^ { 3 }$.\\
\hfill \mbox{\textit{Edexcel C2 2007 Q3 [6]}}