What Makes Up an Algebraic Expression?
Whenever a variable (commonly x or y) is combined with numbers through addition, subtraction, multiplication, division, or exponents, that combination is an algebraic expression. A few quick examples:
Each piece separated by a + or - sign is a term, and whatever number sits directly in front of a variable is that term's coefficient.
Types of Algebraic Expressions
Expressions are named according to how many terms they contain:
| Type | What It Means | Example |
|---|---|---|
| Monomial | Just a single term | 5x², -3ab |
| Binomial | Two terms | x + 4, 3a - b |
| Trinomial | Three terms | x² + 2x + 1 |
| Polynomial | One term or more (the umbrella term) | 4x³ - x + 9 |
Adding and Subtracting Expressions
There's one rule that matters most here: you can only combine like terms, meaning terms built from the exact same variable raised to the exact same power.
Multiplying Expressions
Multiplying expressions relies on the distributive property. For two binomials specifically, FOIL (First, Outer, Inner, Last) gives you an order to work through so nothing gets skipped:
Evaluating an Expression
To evaluate an expression, replace the variable with a specific number and carry out the arithmetic. Take 3x² - 2x + 5 and evaluate it at x = 3:
Simplifying an Expression
Simplifying means reducing an expression to its most compact form. Combine every like term you can find, apply the exponent rules as needed, and work through operations in the standard order: parentheses, then exponents, then multiplication and division, then addition and subtraction (PEMDAS/BODMAS).
Mistakes Worth Watching For
- Combining unlike terms: 3x + 2y is not the same as 5xy, and it doesn't simplify further.
- Forgetting to flip the sign when distributing a negative: -(x - 2) = -x + 2, never -x - 2
- Mishandling coefficients during multiplication: 3x · 2x = 6x² - multiply the coefficients, then add the exponents