Binomial Expansion Calculator

The binomial theorem is one of the elegant cornerstones of algebra, and this calculator brings it to life by expanding a binomial raised to a whole-number power, term by term. Enter the two parts of the binomial, a and b, along with the power n, and it lays out the full expansion: every term, the binomial coefficient in front of it, and the value of each term, finishing with the total. Multiplying out something like a plus b to the power five by hand is slow and error-prone, so the theorem gives a shortcut, and this tool applies it for you. The pattern is beautifully regular. Each term pairs a falling power of a with a rising power of b, the two exponents always adding up to n, and the number in front is the binomial coefficient n choose k, which counts the number of ways of choosing k things from n. Those coefficients are exactly the rows of Pascal's triangle, 1, 3, 3, 1 for the cube, 1, 4, 6, 4, 1 for the fourth power, and so on, so the calculator doubles as a way to read off Pascal's triangle for any row. There are always n plus 1 terms, one for each value of k from zero up to n. This makes the tool genuinely useful for senior school and university students learning the binomial theorem, checking expansions, exploring the link to Pascal's triangle and combinations, or evaluating a binomial numerically. Because it updates as you type, you can watch the coefficients grow and the symmetry of the expansion appear as you change the power. The formula and a worked example are explained below.

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