Binomial theorem explanation of (a+b)^5

1. Binomial Theorem
Example
 
5
a b

?
1

2. Binomial
Theorem
Example   ?
5
a b
  2
 
0
......
a b
 
 
1
......
a b
 
1
1 1
0 0
a b
1 1
a b
 
2
......
a b
 
2 2
a b
1 1

3. Binomial
Theorem
Example   ?
5
a b
  3
 
0
......
a b
 
 
1
......
a b
 
1
1 1
0 0
a b
1 1
a b
 
2
......
a b
 
2 2
a b
1 1
2
2

4. Binomial
Theorem
Example   ?
5
a b
  4
 
2
......
a b
 
2 2
a b
1 1
2
 
2
a b
 
2 0 1 1 0 2
2
a b a b a b
 
2 1 0
a a a
 
0 1 2
b b b
 
2 2
2
a ab b
 

5. Binomial
Theorem
Example   ?
5
a b
  5
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1

6. Binomial
Theorem
Example   ?
5
a b
  6
5 0 4 1 3 2 2 3 1 4 0 5
1 5 10 10 5 1
a b a b a b a b a b a b
5 4 3 2 2 3 4 5
5 10 10 5
a a b a b a b ab b
    