The Binomial Theorem

The Binomial Theorem provides a way to expand expressions raised to a power, like (a + b)^n, into a sum of terms involving a and b. It shows that the expansion is a combination of different powers of a and b multiplied by specific numbers called binomial coefficients. These coefficients form a pattern called Pascal’s Triangle. Each term in the expansion results from choosing a certain number of b’s and a certain number of a’s, multiplied together, and the theorem systematically describes all these possibilities. This makes it easier to find the expanded form without multiplying everything out manually.