Edexcel C4 — Question 29 8 marks

Exam BoardEdexcel
ModuleC4 (Core Mathematics 4)
Marks8
PaperDownload PDF ↗
TopicGeneralised Binomial Theorem
TypeProduct with linear term
DifficultyModerate -0.3 Part (a) is a standard application of the binomial expansion formula for negative powers requiring routine substitution and simplification. Part (b) requires the additional step of multiplying the expansion by (x+4), which involves straightforward algebraic manipulation. This is a typical C4 textbook question testing core technique with minimal problem-solving demand, making it slightly easier than average.
Spec1.04c Extend binomial expansion: rational n, |x|<1

  1. Expand \((1 + 3x)^{-2}\), \(|x| < \frac{1}{3}\), in ascending powers of \(x\) up to and including the term in \(x^3\), simplifying each term. [4]
  2. Hence, or otherwise, find the first three terms in the expansion of \(\frac{x + 4}{(1 + 3x)^2}\) as a series in ascending powers of \(x\). [4]

\begin{enumerate}[label=(\alph*)]
\item Expand $(1 + 3x)^{-2}$, $|x| < \frac{1}{3}$, in ascending powers of $x$ up to and including the term in $x^3$, simplifying each term. [4]

\item Hence, or otherwise, find the first three terms in the expansion of $\frac{x + 4}{(1 + 3x)^2}$ as a series in ascending powers of $x$. [4]
\end{enumerate}

\hfill \mbox{\textit{Edexcel C4  Q29 [8]}}