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Definition 2024

binomial theorem ‎(uncountable)

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

formula giving the expansion of an alegraic sum raised to any positive integer power