AlgebraStructure & Method · Book 1All Chapters

Multiplication

4-5Multiplying Polynomials by Monomials

Overview

Distribute the monomial to every term of the polynomial.

Key ideas

  • Use the distributive property.
  • Combine exponents on like bases.
  • Watch sign of the monomial.

Worked examples

Example 1

Problem. 3x(2x^2 − 5x + 1)

Solution. 6x^3 − 15x^2 + 3x

Example 2

Problem. −2a(a + 4)

Solution. −2a^2 − 8a

Practice

Try each one. Click Show answer when ready.

  1. 1.

    4(x^2 + 3x − 2)

  2. 2.

    −x(2x − 7)

  3. 3.

    5y(y^2 + 2y + 1)

Challenge problems

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

  1. 1.

    Simplify −3x(2x² − 5x + 4).

  2. 2.

    Simplify 2a²b(3ab − 5a² + 2b²).