Tooltip
These resources have been reviewed and selected by STEM Learning’s team of education specialists for factual accuracy and relevance to teaching STEM subjects in UK schools.

# 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.

#### Show health and safety information

Please be aware that resources have been published on the website in the form that they were originally supplied. This means that procedures reflect general practice and standards applicable at the time resources were produced and cannot be assumed to be acceptable today. Website users are fully responsible for ensuring that any activity, including practical work, which they carry out is in accordance with current regulations related to health and safety and that an appropriate risk assessment has been carried out.