What is an Algebraic Expression?
An algebraic expression uses variables (like x or y) combined with numbers and operations (+, -, x, ÷, powers). For example:
3x + 7 | 2a² - 5b + 1 | 4xy/z
The individual pieces separated by + or - are called terms. The number part of a term is the coefficient.
Types of Algebraic Expressions
| Type | Definition | Example |
|---|---|---|
| Monomial | One term only | 5x², -3ab |
| Binomial | Exactly two terms | x + 4, 3a - b |
| Trinomial | Exactly three terms | x² + 2x + 1 |
| Polynomial | One or more terms | 4x³ - x + 9 |
Adding & Subtracting Expressions
Combine like terms, which are terms with the same variable and exponent:
(3x² + 2x - 1) + (x² - 5x + 4) = 4x² - 3x + 3
Multiplying Expressions
Use the distributive property (FOIL for two binomials):
(x + 3)(x - 2) = x² - 2x + 3x - 6 = x² + x - 6
Evaluating Expressions
Substitute the value of the variable and simplify. For example, evaluate 2x² - x + 3 when x = 4:
2(4)² - 4 + 3 = 2(16) - 4 + 3 = 32 - 4 + 3 = 31
Simplifying Expressions
Combine all like terms and apply exponent rules to get to the simplest form. Follow the order of operations: parentheses, then exponents, then multiplication and division, then addition and subtraction (PEMDAS/BODMAS).
Common Mistakes
- Adding unlike terms: 3x + 2y is not 5xy
- Forgetting to distribute a negative sign: -(x - 2) = -x + 2, not -x - 2
- Confusing coefficients: 3x · 2x = 6x² (multiply coefficients and add exponents)