AlgebraStructure & Method · Book 1All Chapters

Products and Factors

5-4Multiplying Binomials Mentally

Overview

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

Key ideas

  • First, Outer, Inner, Last.
  • Combine the middle terms.
  • With practice, you can write the answer directly.

Worked examples

Example 1

Problem. (x + 5)(x + 3)

Solution. x^2 + 8x + 15

Example 2

Problem. (x − 2)(x + 7)

Solution. x^2 + 5x − 14

Practice

Try each one. Click Show answer when ready.

  1. 1.

    (x + 4)(x + 6)

  2. 2.

    (y − 5)(y − 1)

  3. 3.

    (2x + 3)(x + 1)

Challenge problems

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

  1. 1.

    Multiply mentally: (3x − 4)(2x + 5).

  2. 2.

    Multiply mentally: (5a − 2b)(3a + b).