Paper 1 · Algebra
⏱ Tested in 3 exam questions since 2023
Lesson 21 of 23
Algebra 21 – Binomial Theorem
In this lesson you’ll learn to
- Apply the binomial theorem (page 20 of the tables) to expand (x + y)ⁿ
- Write the general term T₍ᵣ₊₁₎ = C(n,r)·xⁿ⁻ʳ·yʳ without expanding
- Find the term independent of x by setting the total power of x to zero
- Find the coefficient of xᵏ using the index laws instead of a full expansion
Formula used
The Binomial Theorem
(x + y)ⁿ = Σ C(n, r) · xⁿ⁻ʳ · yʳ
General term: T(r+1) = C(n, r) · xⁿ⁻ʳ · yʳ
On page 20 of the log tables — read it off, don’t memorise.Most recent exam questions
- 2025 Paper 1 Q5(a) — binomial expansion at low power — either direct multiplication or the binomial theorem w…
- 2025 Paper 1 Q6(a) — binomial theorem applied via the general term formula from page 20 of the log tables
- 2023 Paper 1 Q1(b) — specific-term extraction from a binomial expansion, with a 1/x term inside the bracket —…
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