Algebraic Expressions
Variables and evaluating expressions
lessons (6)
Variables and Algebraic Expressions
Learn what variables are and how to write, read, and evaluate algebraic expressions.
Simplifying Algebraic Expressions
Learn how to simplify algebraic expressions by combining like terms and using properties of operations.
Evaluating Expressions
Learn how to substitute values for variables and calculate the result of algebraic expressions.
Writing Algebraic Expressions
Learn how to translate words and real-world situations into algebraic expressions using variables and operations.
Combining Like Terms
Learn how to simplify algebraic expressions by combining terms with the same variable.
Distributive Property
Learn how to multiply a number or variable by a sum or difference inside parentheses.
Algebraic expressions are the building blocks of algebra. An expression combines numbers, variables, and operations to represent mathematical relationships. Unlike equations, expressions don't have equals signs—they describe quantities that can be simplified, evaluated, or combined. Mastering expressions is essential for all higher mathematics.
In this topic, you will learn to interpret and manipulate algebraic expressions. You will understand how variables represent unknown values and how coefficients and constants work together. Skills like combining like terms, applying the distributive property, and simplifying complex expressions will become second nature.
Our lessons connect expressions to real situations—writing formulas for areas, representing patterns, and modeling relationships. With visual models and interactive practice, you will develop the algebraic fluency needed for equation solving, function analysis, and beyond.
What Students Will Learn
- Identify variables, coefficients, and constants in expressions
- Evaluate expressions by substituting values
- Combine like terms to simplify expressions
- Apply the distributive property correctly
- Translate verbal phrases into algebraic expressions
- Factor common factors from expressions
- Work with expressions containing multiple variables
Frequently Asked Questions
What does a variable represent?
A variable is a letter (like x, y, or n) that represents an unknown or changing value. It allows us to write general formulas and expressions that work for many different numbers.
What are like terms?
Like terms have the same variable raised to the same power. For example, 3x and 7x are like terms (both have x), but 3x and 3x² are not (different powers). Only like terms can be combined.
What is the distributive property?
The distributive property states that a(b + c) = ab + ac. You multiply the outside term by each term inside the parentheses. It's essential for simplifying expressions and solving equations.