The Binomial Theorem ...
Notice the patterns ...
(1) The coefficient of the term is:
(2) The exponent on a is given by: [n - (i - 1)]
(3) The exponent on b is given by: i - 1
(4) This relation holds for each term in the expansion:
[exponent on a] + [exponent on b] = n
(5) The number of terms in any binomial expansion is: n + 1