Newton's Binomial Theorem

Newton's Binomial Theorem provides a way to expand expressions like \((a + b)^n\), where \(n\) is a positive integer. It states that this expansion is a sum of terms, each involving a coefficient, a power of \(a\), and a power of \(b\). These coefficients are called binomial coefficients and are calculated using combinations, which count how many ways to choose items. The theorem offers a formula: \[ (a + b)^n = \sum_{k=0}^n \binom{n}{k} a^{n-k} b^k \] making it easier to expand and analyze powers of sums systematically.