1.Proper nounA formula giving the expansion of a binomial such as
(
a
+
b
)
{\displaystyle (a+b)}
raised to any positive integer power, i.e.
(
a
+
b
)
n
{\displaystyle (a+b)^{n}}
. It's possible to expand the power into a sum of terms of the form
a
x
b
y
c
{\displaystyle ax^{b}y^{c}}
where the coefficient of each term is a positive integer. For example:"
(
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}.}
"