A way of expanding (a + b)ⁿ without multiplying it out. The real exam skill is picking out one specific term without expanding the whole thing, which is what the general term formula is for.
Syllabus points covered
- Use the expansion of (a + b)ⁿ where n is a positive integer
- Use the notation n! and the binomial coefficient nCr
- Find a particular term or coefficient in a binomial expansion
- Apply the expansion in problems involving products of expressions
Common mistakes
- Forgetting that the powers of the two terms must always add to n.
- Dropping the sign when a term is negative — (2 − 3x)ⁿ needs the minus carried into every power.
- Forgetting to raise the numerical coefficient to the power too: (2x)³ is 8x³, not 2x³.
- When asked for the coefficient, giving the whole term instead — or the reverse. Read carefully.
Worksheets
Use these as soon as you've learned the topic and need to practise it. Start with the worksheet, check yourself against the answers, and only then look at the step-by-step solutions.
- Binomials of the form (1 + b)ⁿ
- Binomials of the form (1 + b)ⁿ — answers
- Binomials of the form (a + b)ⁿ
- Binomials of the form (a + b)ⁿ — answers
- Step-by-step solutionsComing soon
Topical past papers
Move on to these once you've worked through the worksheets and are ready for harder, exam-style questions. Real past-paper questions on this topic, with the official mark scheme and full worked solutions.
- Topical questionsComing soon
- Mark schemeComing soon
- Step-by-step worked solutionsComing soon
Looking for whole papers by session? All Additional Mathematics past papers