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.
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.
