Binomial Series Expansion Calculator
Enter a, b, and exponent n to expand (a + b)^n and see every term with its binomial coefficient.
( a + b ) n
Expanded Expression
Term Breakdown
| k | C(n,k) | Term (symbolic) | Numeric value |
|---|
Total (a + b)^n
Pascal's Triangle Row (n = )
Set a, b, and n then click Expand
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Summary
Enter a, b, and exponent n to expand (a + b)^n and see every term with its binomial coefficient.
How it works
- Enter values for a and b (can be integers, decimals, or negative numbers).
- Enter the exponent n (integer from 0 to 10).
- The tool applies the binomial theorem: (a+b)^n = Σ C(n,k) · a^(n-k) · b^k.
- Each term is listed with its binomial coefficient, powers, and simplified value.
- The full expanded expression is shown at the top for easy copying.
Use cases
- Verify manual binomial expansion homework.
- Study Pascal's triangle and how coefficients arise.
- Quickly expand expressions like (x+1)^5 or (2x−3)^4.
- Check intermediate algebra and precalculus textbook problems.
- Understand how binomial coefficients scale with n.
- Generate expansions for probability and statistics formulas.
Frequently Asked Questions
Last updated: 2026-06-13 ·
Reviewed by Nham Vu