Moderate -0.3 This is a standard C2 binomial theorem question requiring students to write out the expansion, form simultaneous equations from given coefficients, and solve for parameters. While it involves multiple steps and solving simultaneous equations, the technique is routine and commonly practiced in textbooks, making it slightly easier than average.
5. (a) Write down the first 4 terms of the binomial expansion, in ascending powers of \(x\), of
$$( 1 + a x ) ^ { n } , n > 2 .$$
Given that, in this expansion, the coefficient of \(x\) is 8 and the coefficient of \(x ^ { 2 }\) is 30 ,
(b) calculate the value of \(n\) and the value of \(a\),
(c) find the coefficient of \(x ^ { 3 }\). [0pt]
[P2 November 2003 Question 3]
5. (a) Write down the first 4 terms of the binomial expansion, in ascending powers of $x$, of
$$( 1 + a x ) ^ { n } , n > 2 .$$
Given that, in this expansion, the coefficient of $x$ is 8 and the coefficient of $x ^ { 2 }$ is 30 ,\\
(b) calculate the value of $n$ and the value of $a$,\\
(c) find the coefficient of $x ^ { 3 }$.\\[0pt]
[P2 November 2003 Question 3]\\
\hfill \mbox{\textit{Edexcel C2 Q5 [8]}}