Binomial Theorem notes
OpenThe 4 formulas you need for Binomial Theorem, on one page.
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Maths · printable
Binomial Theorem: One-Page Formula Sheet
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Last updated: 26 October 2026
Formula sheet
Binomial Theorem formulas
Binomial Theorem — formula sheet
Formulas
- Σ ⁿCᵣ = 2ⁿ
- Sum of even-index coefficients = 2ⁿ⁻¹
- Term independent of x: set power of x to 0
- ⁿCᵣ + ⁿCᵣ₋₁ = ⁿ⁺¹Cᵣ
Key ideas
- General term Tᵣ₊₁ = ⁿCᵣ aⁿ⁻ʳ bʳ
- Middle term: one if n even, two if n odd
- Sum of coefficients: put x = 1
- Greatest coefficient is the middle binomial coefficient
Traps to avoid
- Indexing Tᵣ instead of Tᵣ₊₁
- Sign errors with (a − b)ⁿ
- Forgetting negative powers of x in the general term
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FAQs
Frequently asked questions
Where can I get a Binomial Theorem formula sheet PDF for free?
On this page. Use the print button and choose 'Save as PDF'.
How should I use a formula sheet?
Read it once a day for a week, then cover it and write the formulas from memory. Revise only the ones you missed.