Binomial Expansion Calculator
Enter a nonnegative integer n and two variable names to compute the expansion of (a+b)ⁿ instantly. All calculations happen locally in your browser with no external requests.
Expansion Result
5 termsTerm Coefficients Visualization
How to Use This Calculator
Enter the Exponent
Type a nonnegative integer (0-50) in the n field. This determines the power to which the binomial is raised.
Set Your Variables
Customize the two variables in the formula. The default uses x and y, but you can use any letters or symbols.
Click Expand
Press the Expand button to instantly see the expanded form with all terms.
Copy or Download
Copy the LaTeX code for academic work, or download an SVG image of your expansion.
💡 Pro Tips
- Try n = 0 — Any expression to the power of 0 equals 1
- Try n = 1 — Shows the simple linear form: a + b
- Large n values — Coefficients follow Pascal's Triangle pattern
- Negative exponents — Not supported (use series expansion tools instead)
Frequently Asked Questions
What is the Binomial Theorem?
The Binomial Theorem describes the algebraic expansion of powers of a binomial. For any nonnegative integer n, the expansion of (a + b)ⁿ is the sum of terms of the form C(n,k)·aⁿ⁻ᵏ·bᵏ, where C(n,k) is the binomial coefficient "n choose k".
What range of n can I use?
This calculator supports exponents from 0 to 50. Larger values would produce very long expansions (n=50 has 51 terms) and may slow down the browser. For n > 50, consider using mathematical software.
What are binomial coefficients?
Binomial coefficients C(n,k) = n! / (k!(n-k)!) represent the number of ways to choose k items from n items without regard to order. They form Pascal's Triangle and appear as coefficients in binomial expansions.
Can I use variables with subscripts?
Yes! You can enter variables like a₁, x₂, or even Greek letters like α, β. The calculator treats them as text strings.
What is the LaTeX output for?
The LaTeX button copies the mathematical notation format used in academic papers and typesetting. You can paste it into LaTeX editors, Overleaf, or markdown documents with math support.
Does this work offline?
Yes! All calculations happen entirely in your browser using JavaScript. No data is sent to any server, making it fast, private, and works without an internet connection.