Binomial Theorem Calculator

This binomial theorem calculator expands a binomial power, (a + b) to the n, term by term. Enter a value for a, a value for b, and a whole number power n from 0 to 12, and it instantly returns the sum of every term in the expansion, the total number of terms, and the full list of binomial coefficients used to build each one. The binomial theorem states that (a + b)^n splits into n plus 1 terms, each formed by multiplying a binomial coefficient, n choose k, by a raised to a falling power and b raised to a rising power, and those coefficients match row n of Pascal’s triangle. This makes the tool useful for checking algebra homework, verifying an expansion by hand, exploring how Pascal’s triangle connects to probability, or saving time on a tedious multi-term expansion. Change any of the three inputs and the result, term count and coefficient list update straight away, so you can experiment with different powers and watch how quickly the number of terms and the size of the coefficients grow. Try the worked example below, entering 1, 1 and 4, to check the calculator against a result you can verify by hand, where the coefficients 1, 4, 6, 4 and 1 sum to 16. Results are rounded for display, and n is limited to whole numbers between 0 and 12.

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