Polynomial Multiplication Calculator

About this calculator

Multiplying two polynomials means multiplying every term of the first by every term of the second and then combining like terms — the same distributive process taught as FOIL for two binomials, generalized to any degree. Given coefficient lists ordered from the highest power down, the result's coefficients come from convolving the two input lists: the coefficient of each resulting power is the sum of every pair of input coefficients whose exponents add up to that power.

This calculator takes the coefficients of two polynomials, highest degree first, and returns the fully expanded product polynomial, saving the error-prone manual bookkeeping of larger cross-multiplications by hand. Algebra and precalculus students checking homework, teachers generating answer keys, and engineers doing polynomial-based signal or control-system work — where multiplying polynomials is mathematically the same operation as convolving two signals — use it to verify expansions quickly.