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

x

^{3}+ 3x^{2}Y + 3xY^{2}+ y^{3}x

^{4}+ 4x^{3}Y + 6x^{2}Y^{2}+ 4XY^{3}+ Y^{4}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.