# Binomial Expansion

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

- 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, and is calculated by where ‘!’ donates a factorial function (^{x}C_{y}*e.g.*).5! = 1×2×3×4×5 To calculate the coefficient of the

**z**th 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* Many calculators have a^{11}C_{2}= 55**Choose Function**programmed in them. It might look likenCr .