Monomial. Multiplication of Monomials
Monomial. Multiplication of Monomials
Definition of a Monomial
Monomial — an algebraic expression that is:
- a number (for example: 5, −7, 2.3)
- a variable (for example: x, y, a)
- a product of numbers and variables with natural (positive integer) exponents
✓ Examples of monomials:
5
x
3a
−7x²y
2a³b²c
−ab
✗ These are NOT monomials:
| Expression | Why it is NOT a monomial |
|---|---|
x + y |
Contains addition (this is a polynomial) |
3a − 2 |
Contains subtraction (this is a polynomial) |
5/x or 5x⁻¹ |
Division by a variable (negative exponent) |
√x |
Fractional exponent |
📐 Standard Form of a Monomial
Standard form of a monomial — a notation in which:
- The coefficient (number) comes first
- Variables are written in alphabetical order
- Each variable appears only once with its exponent
Conversion example:
x · 3 · y · x · 2
↓ Group numbers and variables ↓
(3 · 2) · (x · x) · y
↓ Calculate ↓
6x²y — standard form
Not in standard form:
x · 3 · y · x · 2
x · 3 · y · x · 2
Conversion
Standard form:
6x²y
6x²y