Algebraic Expressions: Types, Operations and Examples

An algebraic expression combines numbers, variables and operations without an equals sign. Once you can read its parts, you can simplify it, evaluate it and use it to describe real situations.

Parts of an expression

In 4x² + 3x − 7, the terms are 4x², 3x and −7. The numbers 4 and 3 are coefficients, x is the variable, and −7 is the constant term.

Types

An expression with one term is a monomial, with two terms a binomial, and with three terms a trinomial. An expression with more terms is simply called a polynomial expression.

Operations

Adding and subtracting: combine like terms only. 5x + 3x = 8x, but 5x + 3y cannot be combined further. Multiplying: multiply coefficients and add exponents for the same base. Evaluating: replace the variable with a number. For 2x + 5 with x = 4, the value is 2(4) + 5 = 13.

Example in words

If a notebook costs x and you buy 3 notebooks plus a pen costing 2, the total cost is 3x + 2. That short expression captures the whole situation.

Learn more

For a video explanation of this topic, see Khan Academy Algebra course.