AlgebraStructure & Method · Book 1All Chapters

Multiplication

2-5The Distributive Property

Overview

a(b + c) = ab + ac. Distribute multiplication over addition or subtraction.

Key ideas

  • Multiply the outside factor by every term inside.
  • Used to expand expressions and combine like terms.
  • Works in reverse for factoring.

Worked examples

Example 1

Problem. Expand 4(x + 5).

Solution. 4x + 20

Example 2

Problem. Expand −3(2y − 7).

Solution. −6y + 21

Practice

Try each one. Click Show answer when ready.

  1. 1.

    Expand 6(a + 3).

  2. 2.

    Expand 5(2x − 4).

  3. 3.

    Expand −2(3n + 5).

Challenge problems

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

  1. 1.

    Simplify −3(2x − 5y) + 4(x + 2y).

  2. 2.

    Simplify 2[3(a − 2b) − (a + b)].