Binomial Expansion Calculator

Enter values for a, b, and an exponent n, and this tool expands (a+b)^n term by term using the binomial theorem.

a (first term)

b (second term)

Exponent n

Which term to highlight (0 = first term)

What this calculator does

This tool expands a binomial raised to a power, (a + b)ⁿ, into its full sum of terms, and highlights the value of one specific term you choose.

The method: the binomial theorem

Each term follows C(n,k)·aⁿ⁻ᵏ·bᵏ, where C(n,k) = n! / (k!(n−k)!) is the binomial coefficient (the same numbers found in Pascal’s triangle). Adding every term from k = 0 to k = n reconstructs the full expansion of (a+b)ⁿ.

The exponent n is limited to whole numbers from 0 to 20 to keep the numbers accurate and easy to read.
To see the classic (x+1)ⁿ style expansion, just leave a and b as symbolic placeholders equal to 1 and read off the coefficients directly.

Provided for general educational purposes.

Last reviewed August 2026