Expressions with Variables (Algebraic Expressions)
Learn how letters and numbers work together in mathematics!
What is an Algebraic Expression?
Definition: An algebraic expression is a mathematical expression containing numbers, letters, and operation signs (+, −, ×, ÷).
Letters in algebraic expressions represent numbers. This powerful idea lets us write general rules that work for many different values!
Examples of Algebraic Expressions:
- 3a + 5
- x² − 2x
- 2ab + c
- 7m − 4n + 2
Key Idea:
Algebraic expressions combine arithmetic with letters to create flexible mathematical statements.
Parts of an Algebraic Expression
Every algebraic expression has three main parts:
Variables
x, y, a, b
Letters that represent unknown numbers
Coefficients
3, 5, −2
Numbers multiplying variables
Constants
7, −4, 10
Numbers without variables
Example: Identify parts of 5x + 3
$$\underbrace{\overbrace{\color{#dc3545}{5}}^{\text{coefficient}} \cdot \overbrace{\color{#0d6efd}{x}}^{\text{variable}}}_{\text{term}} + \overbrace{\color{#ffc107}{3}}^{\text{constant}}$$
5 → Coefficient
x → Variable
3 → Constant
The expression 5x + 3 has two terms: 5x and 3.