A-level maths / Pure 1 / Binomial expansion

Binomial expansion

Understand the coefficients, find the term you need and judge when an approximation is useful.

Choose a lesson. Change the models yourself, keep the written steps in view, and use the optional animations at your own pace.

Binomial expansionExpand binomials using Pascal’s triangle, factorials and combinations. Learn the pattern of powers, handle signs and fractions, and simplify exact surd and integer calculations.
Finding binomial coefficientsFind a chosen coefficient without expanding everything. Use the general term, handle reciprocal powers, combine products and solve for unknown constants or exponents.
Binomial approximationsUse a few binomial terms to estimate powers, compare errors and choose a suitable substitution. Includes percentage error, products, growth and independent-trial probability models.

Useful foundations

Review index laws for powers, expanding brackets for multiplication, or algebraic methods for equations and proof.