Binomial Expansion (Edexcel A Level Maths) : Revision Note
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Binomial Expansion
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

Worked Example

Applications of Binomial Expansion
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

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