Binomial expansion

From Wikipedia, the free encyclopedia
Jump to: navigation, search

Binomial expansion uses an expression to make a series. It uses a bracket expression like . There are three binomial expansions.

The formulas[change | change source]

There are basically three binomial expansion formulas:

   1st (Plus)
2nd (Minus)
3rd (Plus-Minus)

We can explain why there are such 3 formulas with a simple expansion of the product:

Using Pascal's triangle[change | change source]

If is an integer (), we use Pascal's triangle.


To expand :

  • find row 2 of Pascal's triangle (1, 2, 1)
  • expand and so the power goes down by 1 each time from to 0 and the power goes up by 1 each time from 0 up to
  • times the numbers from Pascal's triangle with the right terms.


So


For example:


So as a rule:

where is the number at row and position in Pascal's triangle.

Examples[change | change source]