Binomial Formula
The binomial theorem, which states that for any real numbers (x) and (y) and any positive integer (a), the expansion of (a+b)n is given by:
\[(x+y)^a = \sum_{i=0}^{a} \binom{a}{i} x^{a-i} y^i\]
Here, \(\binom{a}{i}\) represents the binomial coefficient, which is the number of ways to choose (i) elements from a set of (a) distinct elements. The binomial coefficient is calculated as:
\[\binom{n}{k} = \frac{n!}{k!(n-k)!}\]