Paper 1 · Algebra
⏱ Tested in 2 exam questions since 2023
Lesson 21 of 23
Algebra 21 – Binomial Theorem
You’ll learn
- 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 P1 Q6(a)
- 2023 P1 Q1(b)(i) — deferred
- 2023 P1 Q1(b)(ii) — deferred
💬 Stuck on something in this lesson?
Send your question with this lesson’s name attached — you’ll get a reply by email.