Binomial expansion

algebraic expansion of powers of a binomial

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

The formulas change

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

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.


For example:


So as a rule:


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

Examples change