AI Math SolverThe binomial theorem expands (a + b)ⁿ into a sum of terms without multiplying step by step. Learn the formula, the binomial coefficients, and the link to Pascal's triangle.
Solve it with the AI Math SolverRaising a binomial to a power by hand is tedious; the binomial theorem does it in one formula. Each term pairs a binomial coefficient with powers of a and b that add up to n.
The coefficients C(n, k) come from Pascal's triangle or the formula n! / (k!(n − k)!). They tell you how many ways each combination of a and b factors appears in the product.
The binomial theorem says (a + b)ⁿ expands into a sum of terms C(n, k)·aⁿ⁻ᵏ·bᵏ for k from 0 to n, where C(n, k) are the binomial coefficients.
The binomial coefficients form the rows of Pascal's triangle. Each coefficient C(n, k) counts the number of ways to choose k items from n.