Binomial Theorem

(a + b)^n = ^nC_0 a^n

(a + b)^n = ^nC_0 a^n + ^nC_1 a^(n-1)b + ^nC_2 a^(n-2)b^2 + ... + ^nC_(n-1)ab^(n-1) + ^nC_n b^n, where n is a positive integer.

The numbers ^nC_r in the expansion

The numbers ^nC_r in the expansion are called binomial coefficients and are given by ^nC_r = n! / r!(n-r)!, for 0 <= r <= n.

The expansion of (a + b)^n

The expansion of (a + b)^n has n + 1 terms, one more than the index.

In successive terms

In successive terms, the power of a decreases by 1 and the power of b increases by 1. In every term, the sum of the powers of a and b is always n.

The coefficients of binomial expansions can

The coefficients of binomial expansions can be arranged in a triangular pattern known as Pascal's triangle, also called Meru Prastara.