Multiplication

4-6Multiplying Polynomials

Overview

Multiply each term of one polynomial by each term of the other. For two binomials, use FOIL.

Key ideas

  • FOIL: First, Outer, Inner, Last.
  • Combine like terms after distributing.
  • Use a table or area model for larger products.

Worked examples

Example 1

Problem. (x + 3)(x − 5)

Solution. x^2 − 5x + 3x − 15 = x^2 − 2x − 15

Example 2

Problem. (2x + 1)(x + 4)

Solution. 2x^2 + 8x + x + 4 = 2x^2 + 9x + 4

Practice

Try each one. Click Show answer when ready.

  1. 1.

    (x + 2)(x + 7)

  2. 2.

    (y − 3)(y − 4)

  3. 3.

    (2a + 5)(a − 1)

Challenge problems

A little tougher — great for test prep. Click Show answer when ready.

  1. 1.

    Simplify (x + 3)(2x² − x + 4).

  2. 2.

    Simplify (2a − b)(3a + 2b − 1).