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.
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 triangleEdit
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 as a rule:
where is the number at row and position in Pascal's triangle.