For a positive integer of \(n\) \[\left(a + b \right)^n = \binom{n}{0} (a)^n(b)^0 + \binom{n}{1} (a)^{n-1} (b)^{1} + \binom{n}{2} (a)^{n-2} (b)^2 + \dots + \binom{n}{r} (a)^{n - r} (b)^{r} + \dots + \binom{n}{n}(a)^{n-n} (b)^{n}\]
General Term
\(T_{r + 1} = \binom{n}{r} (a)^{n-r} (b)^r \)
where&nbsp;\(r\) is an integer increasing by \(1\) every term, such that&nbsp;\(r = 0, 1, 2 , 3, \dots, n\)

For a positive integer of \(n\)
\[\left(a + b \right)^n = \binom{n}{0} (a)^n(b)^0 + \binom{n}{1} (a)^{n-1} (b)^{1} + \binom{n}{2} (a)^{n-2} (b)^2 + \dots + \binom{n}{r} (a)^{n - r} (b)^{r} + \dots + \binom{n}{n}(a)^{n-n} (b)^{n}\]

\(T_{r + 1} = \binom{n}{r} (a)^{n-r} (b)^r \)

where \(r\) is an integer increasing by \(1\) every term, such that \(r = 0, 1, 2 , 3, \dots, n\)

Binomial Theorem

International Baccalaureate Mathematics: Applications and Interpretation Standard Level

General Formula of Binomial Expansion

General Formula of Binomial Expansion