# Decomposition of the Newton Binomial

If we explain in a simple way what a Newton Binomial is, then this is the decomposition of a binomial (a+b) to the power of n. The formula for decomposing into separate terms of an integer non-negative degree of the sum of two variables was known to Indian and Persian mathematicians. Newton derived the binomial formula for the more general case when the exponent is an arbitrary real number. In general, a binomial is an infinite series.

.**Decomposition of the Newton Binomial**

**Newton 's binomial**

( х )

^{}## Newton ‘s Binomial Formula

For a natural number n, the formula has the form:

where,

binomial coefficients, which are combinations of n from k, k=0,1,2,…,n, а “!” – this is the sign of the factorial).