Pengi Editor's Note: This article was originally published by Think Academy. We're sharing it here for educational value. Think Academy is a leading K-12 math education provider.
How to Multiply Monomials in 2 Easy Steps
Multiplying monomials is a key Algebra 1 skill taught in both school and math competitions. Common mistakes include adding instead of multiplying exponents, misidentifying bases, or combining unlike terms.
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, where 6 is the coefficient and x² has base x and exponent 2.
Must-Know: The Exponent Rule for Multiplication
When multiplying terms with the same base:
aᵐ · aⁿ = aᵐ⁺ⁿ
Keep the same base and add the exponents.
Two Steps to Multiply Monomials
Example: 4x²y · 3xy³
Step 1: Multiply the Constants (Coefficients)
4 × 3 = 12
Step 2: Multiply the Variables (Add Exponents)
x² · x = x³
y · y³ = y⁴
Final Answer: 4x²y · 3xy³ = 12x³y⁴
Example Problems
Example 1
Multiply: 5a³b · 2ab²
- Step 1: 5 × 2 = 10
- Step 2: a³ · a = a⁴; b · b² = b³
Answer: 5a³b · 2ab² = 10a⁴b³
Example 2
Multiply: –3x²y⁴ · 2x³y
- Step 1: –3 × 2 = –6
- Step 2: x² · x³ = x⁵; y⁴ · y = y⁵
Answer: –3x²y⁴ · 2x³y = –6x⁵y⁵
Summary
- Multiply the constants (coefficients)
- Multiply each variable by adding exponents
- Keep everything in standard form (alphabetical order)
Learning to multiply monomials builds the foundation for factoring, simplifying expressions, and solving equations in Algebra 1 and beyond.
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