A Bionomial Expansion is a linear polynomial raised to a power, like this (a + b)^{n}. As n increases, a pattern emerges in the coefficients of each term.

The coefficients form a pattern called Pascal's Triangle, where each number is the sum of the two numbers above it.

For example, (3 + x)^{3} can be expanded to 1 × 3^{3} + 3 × 3^{2}x^{1} + 3 × 3^{1}x^{2} + 1 × 3^{0}x^{3} = 27 + 27x + 9x^{2} + x^{3}

There is another what of calculating the coefficients of each term, using Factorials and the Choose Function. The Choose function is written as ^{x}C_{y}, and is calculated by where '!' donates a factorial function (e.g. 5! = 1×2×3×4×5).

To calculate the coefficient of the zth term of a binomial with exponent n, you would calculate ^{n}C_{(z-1)}.
For example, the coefficient of the third term in the expansion (a + b)^{11}is ^{11}C_{2} = 55 Many calculators have a Choose Function programmed in them. It might look like nCr.