Pascal's Triangle and the Binomial Theorem

This Mathcentre booklet explains the structure of Pascal's triangle and demonstrates how it can be used to raise a binomial expression to a power higher than two. For example if students are asked to find (x+1)⁷ it would be very cumbersome to do this by repeatedly multiplying the expression by itself. However by considering the coefficient of the terms and the power to which the expression is raised the pattern of Pascal's triangle can be used to immediately write down the expansion. To find (a+b)⁴, the row beginning 1,4 would be used to give the expansion: (a+b)⁴ = a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴ There are worked examples throughout the booklet, showing complex expansions with fractional coefficients, and exercises for students to practice the techniques.