Binomial Expansion (Edexcel A Level Maths): Revision Note

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 = ⁿC_n = 1

  • ⁿC₁ = ⁿC_n-1 = n

  • ⁿCr = ⁿC_n-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 ⁿC_r

• 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 ⁿC_r

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