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Polynomial Multiplication

Polynomial Multiplication Calculator

How to Multiply Polynomials

Multiplying polynomials involves distributing each term of one polynomial across every term of the other polynomial (the FOIL method for binomials) and then combining like terms. Here's the step-by-step process:

  1. Distribute Each Term

    Multiply each term in the first polynomial by every term in the second polynomial. This is often called the "FOIL" method when multiplying two binomials.

  2. Multiply Coefficients and Add Exponents

    For each pair of terms multiplied together, multiply their coefficients and add their exponents. For example: (3x²)(5x³) = 15x⁵.

  3. Combine Like Terms

    After multiplying all terms, combine terms that have the same variable raised to the same power. Add their coefficients to simplify the expression.

  4. Arrange in Standard Form

    Write the final polynomial in standard form, ordered from the highest degree term to the lowest.

Example:

(2x² + 3x + 1) × (x - 4) Step 1: Distribute each term = 2x²(x) + 2x²(-4) + 3x(x) + 3x(-4) + 1(x) + 1(-4) Step 2: Multiply coefficients and add exponents = 2x³ - 8x² + 3x² - 12x + x - 4 Step 3: Combine like terms = 2x³ + (-8x² + 3x²) + (-12x + x) - 4 = 2x³ - 5x² - 11x - 4 Final Result: 2x³ - 5x² - 11x - 4