| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Generalised Binomial Theorem |
| Type | Product with linear term |
| Difficulty | Moderate -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. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<1 |
\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]}}