A-Level · Maths
Binomial expansion
What is binomial expansion?
Binomial expansion expands (a + b)^n using (a + b)^n = Σ (n choose k) a^(n−k) b^k for positive integer n. For rational/negative n the expansion is an infinite series, valid only for |b/a| < 1. A-Level Maths examines both forms; Further Maths extends to approximations. Sloppy work with the validity condition is a high-frequency lost mark.
Where it appears in exams
- Find the coefficient of x³ in (1 + 2x)⁵.
- Expand (1 − x)^(−1/2) up to and including x² — and state the range of validity.
- Use a binomial expansion to find an approximation for (1.02)¹⁰.
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