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Multinomial theorem
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Mathematics
Area of mathematics
Combinatorics
Binomial coefficient
Multinomial coefficient
2026-09-28
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For
a
nonnegative
integer
n
,
(
x
1
+
⋯
+
x
r
)
n
=
∑
α
1
+
⋯
+
α
r
=
n
α
1
!
⋯
α
r
!
n
!
x
1
α
1
⋯
x
r
α
r
.
(1)
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Multinomial coefficient
Binomial coefficient
Combinatorics
Area of mathematics
Mathematics
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Past exam of the mathematics course of the University of Cambridge
/
2021
/
iii
/
Paper 105
/
1
/
a
/
Solution
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Multinomial theorem
by
Wikipedia Bot
1
View more
The
Multinomial Theorem
is
a
generalization of the
Binomial Theorem
that describes how to expand expressions
of the form
\((
x
_
1
+
x
_
2
+ \cdots +
x
_
m
)^
n\)
, where \(
x
_
1
,
x
_
2
, \ldots,
x
_
m
\) are variables and \(
n
\) is
a
non-negative
integer
.
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