Polynomial Multiplication Calculator

Multiply two polynomials together and see the resulting polynomial.

Polynomial A

Enter coefficients from highest to lowest degree

x^2

const

A(x) = x^2 + 2x + 1

Polynomial B

Enter coefficients from highest to lowest degree

const

B(x) = x + 1

Result: A(x) × B(x)

x^3 + 3x^2 + 3x + 1

Coefficients: [1, 3, 3, 1]

Degree: 3

How It Works

Polynomial multiplication uses the distributive property. Each term of the first polynomial is multiplied by each term of the second polynomial, then like terms are combined.

(a₀xⁿ + a₁xⁿ⁻¹ + ...) × (b₀xᵐ + b₁xᵐ⁻¹ + ...) = Σᵢⱼ aᵢbⱼxⁿ⁺ᵐ⁻ⁱ⁻ʲ