🧩 Algebraic Expressions

What is an Algebraic Expression?
An algebraic expression is a mathematical phrase that contains numbers, variables (letters), and operations (+, -, ×, ÷). It does NOT have an equals sign.
Variable: A letter that represents an unknown number (like x, y, n, a)
Key Words for Operations:
OperationKey WordsExampleExpressionAddition (+)plus, more than, sum, increased by, total5 more than a numberx + 5Subtraction (-)minus, less than, difference, decreased by, fewer3 less than a numberx - 3Multiplication (×)times, product, of, twice, tripletwice a number2xDivision (÷)divided by, quotient, half, splithalf of a numberx/2 or x÷2Important Order Notes:
• "5 more than a number" → x + 5
• "5 less than a number" → x - 5 (NOT 5 - x!)
• "Twice a number" → 2x
• "A number divided by 3" → x/3

What Does "Evaluate" Mean?
To evaluate an expression means to substitute (replace) the variable with a number and then calculate the result.
Steps to Evaluate:
• Write the expression
• Replace each variable with its given value (use parentheses!)
• Follow order of operations (PEMDAS)
• Simplify to get a single number

Example: Evaluate 3x + 4 when x = 6
• Write: 3x + 4
• Substitute: 3(6) + 4
• Calculate: 18 + 4 = 22

What are Like Terms?
Like terms are terms that have the exact same variable raised to the exact same power.
Like Terms Examples:
• 3x and 5x (same variable x)
• 2y² and 7y² (same y²)
• 4 and 9 (constants with no variable)

NOT Like Terms:
• 3x and 3y (different variables)
• 2x and 2x² (different exponents)

How to Combine Like Terms:
Add or subtract the coefficients (numbers in front), keep the variable the same.
3a + 5a = (3 + 5)a = 8a
7b - 2b = (7 - 2)b = 5b
4x² + 2x² = (4 + 2)x² = 6x²