Binomial Theorem (Step-by-Step)

​
n
2
3
4
5
6
4
(x+y)
=
4
∑
k=0

4
k

k
x
4-k
y
=

4
0

0
x
4-0
y
+
4
1

1
x
4-1
y
+
4
2

2
x
4-2
y
+
4
3

3
x
4-3
y
+
4
4

4
x
4-4
y
=
4
y
+4x
3
y
+6
2
x
2
y
+4
3
x
y+
4
x
The binomial theorem says that for positive integer n,
n
(x+y)
=
n
∑
k=0

n
k

k
x
n-k
y
, where

n
k
=
n!
k!(n-k)!
. This widely useful result is illustrated here through termwise expansion.

External Links

Binomial Theorem (Wolfram MathWorld)

Permanent Citation

Bruce Colletti, Jeff Bryant
​
​"Binomial Theorem (Step-by-Step)"​
​http://demonstrations.wolfram.com/BinomialTheoremStepByStep/​
​Wolfram Demonstrations Project​
​Published: December 12, 2007