Moderate -0.3 This is a straightforward binomial expansion question requiring standard application of the binomial theorem formula. Part (a) is routine recall of the expansion formula, and part (b) involves setting up and solving a simple equation from the coefficient condition. The algebra is uncomplicated (quadratic equation) and the question follows a very standard template with no novel insight required.
10. (a) Find the first 4 terms, in ascending powers of \(x\), in the binomial expansion of
$$( 1 + k x ) ^ { 10 }$$
where \(k\) is a non-zero constant. Write each coefficient as simply as possible.
Given that in the expansion of \(( 1 + k x ) ^ { 10 }\) the coefficient \(x ^ { 3 }\) is 3 times the coefficient of \(x\), (b) find the possible values of \(k\). [0pt]
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10. (a) Find the first 4 terms, in ascending powers of $x$, in the binomial expansion of
$$( 1 + k x ) ^ { 10 }$$
where $k$ is a non-zero constant. Write each coefficient as simply as possible.
Given that in the expansion of $( 1 + k x ) ^ { 10 }$ the coefficient $x ^ { 3 }$ is 3 times the coefficient of $x$, (b) find the possible values of $k$.\\[0pt]
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\hfill \mbox{\textit{SPS SPS FM Pure 2023 Q10 [6]}}