Algebraic Expressions — Types, Operations and Examples

An algebraic expression is a combination of numbers, variables (letters), and operations like addition, subtraction, multiplication and division. Unlike an equation, an expression has no equals sign — you simplify or evaluate it, you don't "solve" it.

3x + 2,    5a − 7b,    x² + 4x − 9

The parts of an expression

Take 7x² − 3x + 5:

• Variable — the letter that stands for an unknown value (x).
• Term — a single number or variable piece separated by + or −: 7x², −3x, 5.
• Coefficient — the number multiplying a variable: 7 and −3.
• Constant — a term with no variable: 5.

Types of algebraic expressions

By the number of terms:

• Monomial — one term: 4x
• Binomial — two terms: 3x + 2
• Trinomial — three terms: x² + 5x + 6

(See our full guide on the types of polynomials for the degree-based classification too.)

Like terms — the key to simplifying

Like terms have the same variable raised to the same power. You can combine them; you can't combine unlike terms.

3x + 5x = 8x          (like terms)
3x + 5x² → stays as is (unlike terms)
4a + 2b − a = 3a + 2b

Adding and subtracting expressions

Combine like terms, watching the signs:

(2x² + 3x − 1) + (x² − 5x + 4)
= (2x² + x²) + (3x − 5x) + (−1 + 4)
= 3x² − 2x + 3

When subtracting, distribute the minus sign to every term first:

(5x − 2) − (3x + 4)
= 5x − 2 − 3x − 4
= 2x − 6

Multiplying expressions

Use the distributive property, then combine like terms:

2x(3x + 4) = 6x² + 8x
(x + 3)(x + 2) = x² + 2x + 3x + 6 = x² + 5x + 6

That last expansion is exactly the reverse of factoring — see how to factor polynomials.

Evaluating an expression

To evaluate, substitute a value for the variable and compute, following the order of operations. Evaluate x² + 4x − 9 at x = 3:

3² + 4(3) − 9 = 9 + 12 − 9 = 12

You can check substitutions quickly with the scientific calculator.

Expression vs. equation

The moment you add an equals sign, an expression becomes an equation you can solve. 3x + 2 is an expression; 3x + 2 = 8 is an equation (with solution x = 2). Mastering expressions is what makes solving equations feel easy.