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The binomial expansion for a positive integer power lets you expand (a + b)ⁿ using Pascal's triangle and the nCr coefficients without multiplying out every bracket, and to find specific terms and coefficients quickly. It appears across A-Level and iAL Pure Maths with the major exam boards. Work through it free on eClassroom, with clear worked examples and instantly-marked questions that build your confidence for the exam.
How you do it
Expand using the binomial coefficients from Pascal's triangle or the nCr button. Powers of the first term count down and the second count up, and the two always add to n. For a specific term, use the general term rather than expanding everything.
Before you start
Best tackled after index laws and combinations. It leads on to approximation and the general term.
What you learn
You'll expand with negative and fractional coefficients, pick out single terms, compare coefficients to find unknowns, reuse an expansion inside a product, and use expansions to approximate powers. The course works through the expansion and Pascal's triangle, negative and fractional coefficients, finding a specific term, comparing coefficients, products: expand, then use it and approximations. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
We teach Binomial Expansion (C12) as one of the Sequences & Series topics in our A-level course library, at the AS year. You work through 6 concepts and 6 worked examples, testing yourself at 6 points. Students often pair it with Binomial Expansion (C34), Geometric Sequences, Geometric Series, Recurrence Relations and Arithmetic Sequences. For unlimited practice, the Sequences & Series revision engine builds new questions on demand and records your accuracy.
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