What is the binomial expansion?
- Look at the pattern
- Start at nC0, then nC1, nC2, etc
- Powers of a start at n and decrease by 1
- Powers of b start at 0 and increase by 1
- There are shortcuts but these hide the pattern
- nC0 = nCn = 1
- nC1 = nCn-1 = n
- nCr = nCn-r
- (b)0 = (a)0 = 1
- Use the shortcuts once familiar with the pattern
- ! means factorial
- This is given in the formula booklet
What about Pascal’s triangle?
- Pascal’s triangle is an alternative to nCr
- It is useful for lower values of n
- For larger n it is slow and prone to arithmetic errors
How do I expand brackets with binomial expansion?
- Use a line for each term to make things easier to read and follow
- Use brackets, particularly helpful when negatives involved
- Use a calculator for nCr
What are binomial expansions used for?
- Expanding brackets, it is usual to be asked for either …
- … the first few terms only
- or (the coefficient of) a particular term
- Solving problems in unknowns