What name refers to a theorem that gives a formula to expand (a+b)^n without repeated multiplications?

• A. Binomial Theorem
• B. Factor Theorem
• C. Theorem
• D. Pascal's Triangle

Answer: (A)

The main idea here is recognizing the named result that provides a direct formula for expanding a binomial raised to any power. This is the Binomial Theorem. It shows how to write (a+b)^n as a sum of n+1 terms with coefficients given by the binomial coefficients, so you don’t multiply step by step. In formula form, (a+b)^n equals a^n + nC1 a^{n-1}b + nC2 a^{n-2}b^2 + ... + nC{n-1}ab^{n-1} + b^n, with nCk coming from binomial coefficients (often found in Pascal’s Triangle). This theorem precisely provides the expansion directly, whereas the other concepts either deal with factoring, are generic, or relate to the triangle as a tool rather than the expansion rule itself.