A Level Maths: Binomial Expansion Topic Summary and Resources
Video Lessons
Watch alongside the worksheet for the full lesson experience, then test your understanding with the lesson questions.
Revision Notes
Handwritten notes summarising the key ideas for each lesson. Ideal for quick review before a test.
Exam Questions
Past-paper-style questions organised by topic, with full mark schemes.
Drawn from OCR and Edexcel past papers but designed to be useful for students of all UK exam boards — including AQA and OCR MEI — unless a sheet is explicitly board-specific.
Before You Start This Topic
It will help if you are confident with the following:
- Indices — index laws are needed for every term of the expansion
- Quadratic Equations — expanding brackets and combining like terms is the foundation
- GCSE Maths Algebra — comfort with terms, coefficients, and powers is essential
A Level Maths binomial expansion is the technique for expanding $(a + bx)^n$ for positive integer $n$ without multiplying out every bracket. It is a high-value topic in Pure Maths: a well-defined, formula-driven topic that rewards practice. The technique also previews ideas you will see in General Binomial Expansion and in series approximations.
You expand using Pascal's triangle for small $n$, and the formula involving $\binom{n}{r}$ (or '$n$ choose $r$') for larger $n$: $(a + bx)^n = \sum_{r=0}^{n} \binom{n}{r} a^{n-r} (bx)^r$. You learn to find specific terms — for example, the coefficient of $x^4$ in $(3 + 2x)^7$ — without writing out the full expansion. You handle expansions with negative or fractional coefficients inside the bracket, and combine the binomial expansion with substitution to evaluate approximations like $(1.02)^{10}$. Mastering binomial expansion also supports later work in Sequences and Series and General Binomial Expansion.
Binomial expansion is part of the Pure Maths strand of A Level Maths and is essential revision content for AQA, Edexcel, OCR, and OCR MEI students.
Watch out for…
A few things to be careful with: $\binom{n}{r}$ counts from $r = 0$, so the $(r+1)$th term has $\binom{n}{r}$ — be careful which term the question is asking for; when expanding $(a + bx)^n$, every term has a power of $a$ AND a power of $bx$, so do not forget the $a^{n-r}$ factor; with negative coefficients like $(3 – 2x)^n$, the signs alternate — track them carefully; and when extracting a coefficient of $x^k$, include any numeric factors like $2^k$ from the $(bx)^k = b^k x^k$ step.