Apply the binomial expansion formula to any power up to 12. Enter a binomial like (2x-3y)^5 and see Pascal's Triangle, the coefficient for every term, and the fully simplified expansion step by step.
The Binomial Expansion Term-by-Term Tableau applies the binomial expansion formula (the Binomial Theorem) to any binomial raised to a power from 0 to 12. Enter an expression like (2x-3y)^5 and see Pascal's Triangle with the matching row highlighted, a row-by-row tableau pairing each binomial coefficient with its powers of A and B, and the fully simplified polynomial.
Every coefficient is computed with exact integer arithmetic, so even (99x-99y)^12 comes out to the last digit. Like terms are combined automatically when both terms share a variable.
The binomial expansion formula, also called the Binomial Theorem, says that (A + B)^n is the sum from k = 0 to n of C(n, k) * A^(n-k) * B^k. The C(n, k) values are the binomial coefficients and the expansion always has n + 1 terms.
Row n of Pascal's Triangle lists C(n, 0) through C(n, n) from left to right, and each entry is the sum of the two above it. Row 5 reads 1, 5, 10, 10, 5, 1 — exactly the coefficients of (A + B)^5.
The second term is negative, so B^k is negative for odd k and positive for even k. That flips the sign of every other term across the expansion.
Use the general term C(n, k) * A^(n-k) * B^k. Counting starts at k = 0, so the third term of (2x - 3y)^5 is the k = 2 row of the tableau.
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