Integer a and b from -1,000 to 1,000 and integer n from 0 to 12.
Binomial Expansion Calculator
Enter your values below to get the result first, then scroll for the full explanation and guidance.
Expanded polynomial
x^3 + 3x^2 + 3x + 1(ax + b)^3
Expanded polynomial: x^3 + 3x^2 + 3x + 1 ((ax + b)^3)
Each coefficient is generated from the binomial coefficient and the corresponding powers of a and b.
Binomial expansion
Each coefficient is generated from the binomial coefficient and the corresponding powers of a and b.
Result snapshot
A quick visual read of the values behind this result.
Coefficient sequence1, 3, 3, 1
Recommended next checks
- →The calculator supports integer coefficients and non-negative exponents up to 12.
- Coefficient sequence
- 1, 3, 3, 1
Try different values to compare results.
Expand (ax + b)^n exactly for integer coefficients and a non-negative exponent up to 12.
Expanded polynomial
x^3 + 3x^2 + 3x + 1(ax + b)^3
Expanded polynomial: x^3 + 3x^2 + 3x + 1 ((ax + b)^3)
Each coefficient is generated from the binomial coefficient and the corresponding powers of a and b.
Binomial expansion
Each coefficient is generated from the binomial coefficient and the corresponding powers of a and b.
Result snapshot
A quick visual read of the values behind this result.
Coefficient sequence1, 3, 3, 1
Recommended next checks
- →The calculator supports integer coefficients and non-negative exponents up to 12.
- Coefficient sequence
- 1, 3, 3, 1
Try different values to compare results.
Table of Contents
Table of Contents
About Binomial Expansion Calculator
Binomial Expansion Calculator helps you work through the main numbers for this topic quickly with a simple input flow and an instant result.
Use the calculator result as a practical starting point, then review the explanation and assumptions on the page if you want more context.
Calculation method
Use the binomial theorem with coefficients choose(n,k) a^(n-k) b^k.
Formula explained
Calculation flow
This calculator is structured for fast UK-focused estimates with clear inputs, repeatable logic, and instant results.
Formula
Input values -> calculation engine -> instant result
How the result is built
1Enter the values requested in the form.
2The calculator applies the configured formula logic.
3The result updates instantly with a breakdown.
4Use the output to compare scenarios quickly.
Example
Example verified by the calculator's polynomial algebra reference cases.
Assumptions
- Integer a and b from -1,000 to 1,000 and integer n from 0 to 12.
Source basis
- UK-focused calculator flow
- Structured input validation
- Instant result breakdowns
FAQ
Common questions
Trust and notes
Assumptions and important notes
This calculator is designed to give a fast estimate using the method shown on the page. Results are most useful when your inputs are accurate and the tool matches your situation.
Use the result as guidance rather than a final diagnosis or professional decision. If the result could affect health, legal, financial, or compliance decisions, verify it with a qualified source where appropriate.
- Integer a and b from -1,000 to 1,000 and integer n from 0 to 12.
Method
UK calculator guidance
Last reviewed
April 17, 2026