Multiplying polynomials

Math

Definition

The process of multiplying two or more polynomials by distributing each term of one polynomial to every term of the other, then combining like terms. For binomials, the FOIL method (First, Outer, Inner, Last) is a common shortcut.

How It Works

  1. Distribute each term of the first polynomial to every term of the second.
  2. Multiply the coefficients and add the exponents of like bases.
  3. Combine like terms.
  4. Write the result in standard form (descending order of degree).

Examples

  • (x + 3)(x + 5) = x² + 8x + 15 using FOIL
  • (2x − 1)(x² + 3x + 4) = 2x³ + 6x² + 8x − x² − 3x − 4 = 2x³ + 5x² + 5x − 4
  • (a + b)² = a² + 2ab + b²
Key Fact

FOIL: (a+b)(c+d) = ac + ad + bc + bd

Related Terms

Polynomial operations Combining like terms Factoring trinomials Difference of squares

Study This Concept

Practice multiplying polynomials with free review games in these units:

Algebra 1 Unit 6: Exponents and Polynomials