Work out polynomial multiplication instantly with clear inputs, formula shown and shareable results.
Multiplying polynomials convolves their coefficient lists: every term of the first multiplies every term of the second, and like powers are collected. The degree of the product is the sum of the two degrees.
Polynomial product
cₖ = Σⱼ aⱼ · bₖ₋ⱼ, deg(AB) = deg A + deg B
2x³ − 5x² − 2x + 15.
The direct method needs (m+1)(n+1) products; fast transforms do better for very large polynomials.