Multiplying monomials is a key Algebra 1 skill taught in both school and math competitions. But students often make mistakes—like adding instead of multiplying exponents, misidentifying bases, or combining unlike terms. Even a small sign error can lead to the wrong answer.

In this guide, we break it down into 2 easy steps, with clear examples to build accuracy and confidence. Free practice worksheets are included at the end.

What Is a Monomial?

A monomial is a math expression that has just one term. It can be:

• A number (like 5),
• A variable (like x),
• Or a product of numbers and variables (like 3x²y).

Example:

6x² is a monomial.

• The number 6 is called the coefficient.
• The variable x² tells us the base is x and the exponent is 2.

Must-Know Before Multiplying Monomials

Before we begin, the Exponent Rule for Multiplication is a must-know prerequisite. When multiplying terms with the same base:

aᵐ · aⁿ = aᵐ⁺ⁿ

This means we keep the same and then add the exponents together. We will use this rule to multiply monomials.

Now, let’s use an example to show how to multiply the monomials clearly:

4x²y · 3xy³

Two Steps to Multiply Monomials

Step 1: Multiply the Constants

Multiply the numbers in front (the coefficients):

4 × 3 = 12

Step 2: Multiply the Variables

Multiply the variables by adding exponents:

x² · x = x³

y · y³ = y⁴

So the final result is:

4x²y · 3xy³ = 12x³y⁴

Example Problems: Multiplication of Monomials

Example 1

Problem:

Multiply

5a³b · 2ab²

Solution:

Step 1: Multiply the constants

5 × 2 = 10

Step 2: Multiply variables

a³ · a = a⁴

b · b² = b³

Answer:

5a³b · 2ab² = 10a⁴b³

Example 2

Problem:

Multiply

–3x²y⁴ · 2x³y

Solution:

Step 1: Multiply the constants

–3 × 2 = –6

Step 2: Multiply variables

x² · x³ = x⁵

y⁴ · y = y⁵

Answer:

–3x²y⁴ · 2x³y = –6x⁵y⁵

Summary: How to Multiply Monomials

Here’s our quick checklist every time we multiply monomials:

1. Multiply the constants (coefficients).
2. Multiply the variable by the exponent rule for multiplication.
3. Keep everything neat and in standard form (alphabetical order helps).

Learning to multiply monomials builds the foundation for topics like factoring, simplifying expressions, and solving equations in Algebra 1 and beyond.

Want more printable worksheets for practicing?

To access more printable worksheets on other math topics, visit this page.

Additional Math Topics for Multiplication – with Free Worksheets

• Grade 2 & 3:
  • How to Multiply 2-Digit by 1-Digit Numbers in 3 Simple Steps
  • Multiplication: Examples, Charts, and MK Applications
• Grade 6: How to Multiply Fractions in 3 Simple Steps
• Algebra 1:
  • How to Multiply Polynomials: From 1 Term to 3 Terms
  • Polynomial Multiplication in Algebra: Formulas, Examples, and AMC 10 Applications

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