Multiplying out (x + y)² by hand is easy; (x + y)⁷ is a punishment — unless you know the binomial theorem, which expands (a + b)ⁿ into a sum of terms with binomial coefficients doing the heavy lifting: (a+b)ⁿ = Σ C(n,k) a^(n-k) b^k. Each term's exponents always add to n, the coefficients come straight from Pascal's triangle, and the signs alternate if it is (a - b)ⁿ. So (x + y)³ becomes x³ + 3x²y + 3xy² + y³, with the 1-3-3-1 row of the triangle staring back at you. Algebra students expand these to simplify expressions, probability students recognize the same coefficients in binomial distributions, and calculus students meet the generalized version in infinite series. The number-one mistake is forgetting that the exponents descend on a while ascending on b — write both sequences explicitly and the pattern holds. This calculator performs the expansion arithmetic: enter your values in the Variable A and Variable B fields and read the Result.

With the pre-filled defaults — Variable A 10, Variable B 5 — the Binomial Expansion Calculator returns Result 50.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.