WOLFRAM|DEMONSTRATIONS PROJECT

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.