In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the polynomial (x + y)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. For example (for n = 4),
(
x
+
y
)
4
=
x
4
+
4
x
3
y
+
6
x
2
y
2
+
4
x
y
3
+
y
4
.
{\displaystyle (x+y)^{4}=x^{4}+4x^{3}y+6x^{2}y^{2}+4xy^{3}+y^{4}.}
The coefficient a in the term of axbyc is known as the binomial coefficient
(
n
b
)
{\displaystyle {\tbinom {n}{b}}}
or
(
n
c
)
{\displaystyle {\tbinom {n}{c}}}
(the two have the same value). These coefficients for varying n and b can be arranged to form Pascal's triangle. These numbers also arise in combinatorics, where
(
n
b
)
{\displaystyle {\tbinom {n}{b}}}
gives the number of different combinations of b elements that can be chosen from an n-element set. Therefore
(
n
b
)
{\displaystyle {\tbinom {n}{b}}}
is often pronounced as "n choose b".