Pascal's Triangle for expanding Binomials

How to use Pascal's Triangle to perform Binomial Expansions

Pascal's Triangle is probably the easiest way to expand binomials. It's much simpler to use than the Binomial Theorem, which provides a formula for expanding binomials. Pascal noticed

The formula for Pascal's Triangle comes from a relationship that you yourself might be able to see in the coefficients below.

(x + y)0
(x + y)1
(x + y)²
(x + y)3
(x + y)4
1
x + y
x² + 2xy + y²
x3 + 3x2Y + 3xY2 + y3
x4 + 4x3Y + 6x2Y2 + 4XY3 + Y4

The demonstration below illustrates the pattern. Pascal's Triangle presents a formula that allows you to create the coefficients of the terms in a binomial expansion.