$Binomial and Pascal’s Triangle$

Binomial and Pascal’s Triangle

The expansion of a binomial and rows of Pascal’s triangle with exact coefficients.

What to find:

Expand (p·a + q·b)ⁿ

Pascal’s triangle

Row n of the triangle

Expansion up to n = 30, the triangle up to row 20, a single row up to n = 200. Rows are numbered from zero. All values are exact.

This calculator expands the binomial (p·a + q·b)ⁿ, builds Pascal’s triangle and shows its individual rows. The coefficients are exact.

(x + y)ⁿ = Σ C_n^k · x^n−k · y^k

Example. (a + b)³ = a³ + 3a²b + 3ab² + b³. The coefficients 1, 3, 3, 1 are row 3 of Pascal’s triangle.

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