AlgebraStructure & Method · Book 1All Chapters

Multiplication

4-3Multiplying Monomials

Overview

Multiply coefficients, then multiply variables by adding exponents.

Key ideas

  • (ax^m)(bx^n) = ab · x^(m+n).
  • Apply to each variable separately.
  • Negative coefficients follow sign rules.

Worked examples

Example 1

Problem. (3x^2)(4x^5)

Solution. 12x^7

Example 2

Problem. (−2a^3)(5a)

Solution. −10a^4

Practice

Try each one. Click Show answer when ready.

  1. 1.

    (6x)(2x^3)

  2. 2.

    (−4y^2)(−3y^5)

  3. 3.

    (2a^2b)(3ab^4)

Challenge problems

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

  1. 1.

    Simplify (−2x²y)(3xy³)(−x).

  2. 2.

    Simplify (4a²b)(−3ab²)(2a).