Variables and Expressions
Algebra uses letters (variables) to represent unknown or changing quantities. An expression is a combination of numbers, variables, and operations — but no equals sign. Expressions can be evaluated (when you know the variable's value) or simplified (combined like terms).
Key Concepts
Variables
A variable is a letter that stands for a number. x, y, n, t are common choices. 3x means 3 times x. If x = 5, then 3x = 15. Variables let us write one rule that works for all values.
Like Terms
Terms with the same variable and exponent are 'like terms' and can be combined. 3x + 5x = 8x. 4x + 2y cannot be combined (different variables). 3x² + 2x cannot be combined (different exponents). Always simplify by combining like terms.
The Distributive Property
a(b + c) = ab + ac. This is used constantly in algebra. 3(x + 4) = 3x + 12. Always distribute before combining like terms. Going in reverse — factoring out a common factor — is equally important: 6x + 10 = 2(3x + 5).
🆕 Expression Evaluator
Enter an expression and a value for x to evaluate it.
✅ Check Your Understanding
1. What is a variable?
2. Simplify: 4x + 7 + 2x − 3
3. What does the distributive property say about a(b+c)?