Binomial Expansion

  • 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 × 33 + 3 × 32x1 + 3 × 31x2 + 1 × 30x3 = 27 + 27x + 9x2 + x3

  • There is another what of calculating the coefficients of each term, using Factorials and the Choose Function. The Choose function is written as xCy, 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 nC(z-1). For example, the coefficient of the third term in the expansion (a + b)11is 11C2 = 55 Many calculators have a Choose Function programmed in them. It might look like nCr.

Written by Sam Adam-Day.