The formula by which any positive integral power of a binomial expression can be expanded in the form of a series is known as Binomial Theorem. If x, y ∈ R and n∈N, then
(x + y)n = nC0 xn + nC1 xn-1 y + nC2 xn-2y2 + ….. + nCrxn-r yr + ….. + nCnyn =nCr xn – r yr
This theorem can be proved by Induction method.
(i) The number of terms in the expansion is (n + 1) i.e. one or more than the index.
(ii) The sum of the indices of x & y in each term is n.
(iii) The binomial coefficients of the terms nC0, nC1…….. equidistant from the beginning and the end are equal. Read more