Learning Monomials
What is a Monomial?
A monomial is a single-term algebraic expression consisting of:
7x²
↙
Coefficient
(constant value)
7
↘
Main Term
(power or product of powers)
x²
Coefficient
Constant value
Examples: 2, 5, -3
Main Term
Power or product of powers
Examples: x, x², xy
Similar (Like) Terms
Monomials that have the same main terms are called similar or like terms.
Examples of similar terms:
- 2x i 3x
- 5x² i -2x²
- 7xy i 4xy
Common Mistakes and Tips
When are terms NOT similar?
x² i x³
Different powers - NOT similar
xy i x²y
Different powers - NOT similar
3x i 3y
Different variables - NOT similar
Useful Tips
- Always check if terms are similar before adding or subtracting
- When multiplying powers with same base, add the exponents
- When dividing powers with same base, subtract the exponents
- Check if you copied all variables with their powers
Basic Operations with Monomials
Addition and Subtraction
Only similar terms can be added or subtracted!
Add or subtract coefficients, keep the main term.
Examples:
- x + x = 2x
- 2x + 3x = 5x
- 5x² - 3x² = 2x²
- 7xy - 3xy = 4xy
Multiplication
When multiplying monomials:
- Multiply coefficients together
- Multiply main terms according to power rules
Examples:
- 3x² × 5x = 15x³
- 4a²b × 3ab² = 12a³b³
Division
When dividing monomials:
- Divide coefficients
- Divide main terms according to power rules
Examples:
- 12x³ : 6x = 2x²
- 2x : 2y = x/y
Step by Step Examples
Example 1: Subtracting terms
7xy - 3xy = 4xy
- Check if terms are similar (yes, both have xy)
- Keep the common part (xy)
- Subtract coefficients (7-3 = 4)
- Write the result (4xy)
Example 2: Multiplying terms
3x² × 2x = 6x³
- Multiply coefficients (3 × 2 = 6)
- Add exponents (x² × x = x²⁺¹ = x³)
- Write the result (6x³)
Check Your Knowledge
Are these terms similar?
- 5x² i 3x² (DA/YES)
- 2xy i 2x²y (NE/NO)
- 4ab i 7ab (DA/YES)
What is the coefficient?
- 7x²y → 7
- -3ab → -3
- xy → 1
What is the main term?
- 7x²y → x²y
- -3ab → ab
- 5x³ → x³
Printable Summary
Definition
Monomial = coefficient × main term
- Coefficient is a constant value (e.g., 2, 5, -3)
- Main term is a power or product of powers (e.g., x, x², xy)
Similar Terms
- Have the same main terms
- Can be added and subtracted
- Examples: 2x and 3x, 5x² and -2x²
Rules for Operations
- Addition/Subtraction: only similar terms, operate on coefficients
- Multiplication: coefficients × coefficients, add exponents
- Division: coefficients ÷ coefficients, subtract exponents
Quick Check
- Are the terms similar? (same main terms)
- What are the coefficients?
- What are the main terms?
- Did I copy all variables and powers correctly?