# binomial theorem

1. (mathematics) A formula giving the expansion of a binomial such as ${\displaystyle (a+b)}$ raised to any positive integer power, i.e. ${\displaystyle (a+b)^{n}}$. It's possible to expand the power into a sum of terms of the form ${\displaystyle ax^{b}y^{c}}$ where the coefficient of each term is a positive integer. For example:
${\displaystyle (x+y)^{4}\;=\;x^{4}\,+\,4x^{3}y\,+\,6x^{2}y^{2}\,+\,4xy^{3}\,+\,y^{4}.}$