Binomial theorem
In elementary algebra, the
binomial theorem describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the power
n into a sum involving terms of the form
axbyc, where the exponents
b and
c are nonnegative integers with
b +
c =
n, and the coefficient
a of each term is a specific positive integer depending on
n and
b. When an exponent is zero, the corresponding power is usually omitted from the term. For example, The coefficient
a in the term of
axbyc is known as the binomial coefficient or . These coefficients for varying
n and
b can be arranged to form Pascal's triangle. These numbers also arise in combinatorics, where gives the number of different combinations of
b elements that can be chosen from an
n-element set.