Lesson 3 • 35 min read
Algebraic Expressions
In This Lesson
1Key Terms
Variable
A letter that represents an unknown value. Can change or vary.
Coefficient
The number multiplied by a variable.
In -5y, the coefficient is -5
In x (alone), the coefficient is 1
Constant
A fixed number that doesn't change. Has no variable attached.
Term
Parts of an expression separated by + or - signs.
2Parts of an Expression
Example Breakdown: 4x² + 3x - 7
| Term | Coefficient | Variable | Type |
|---|---|---|---|
| 4x² | 4 | x² | Variable term |
| 3x | 3 | x | Variable term |
| -7 | N/A | None | Constant term |
Expression Types by Number of Terms
Monomial
1 term: 5x
Binomial
2 terms: 3x + 2
Trinomial
3 terms: x² + 2x + 1
3Translating Verbal to Algebraic
Key Words to Know
Addition (+)
- • sum of
- • plus
- • more than
- • increased by
- • added to
- • total
Subtraction (-)
- • difference of
- • minus
- • less than
- • decreased by
- • subtracted from
- • fewer than
Multiplication (×)
- • product of
- • times
- • multiplied by
- • twice (×2)
- • triple (×3)
- • of
Division (÷)
- • quotient of
- • divided by
- • ratio of
- • per
- • split into
Translation Examples
| Verbal Phrase | Algebraic Expression |
|---|---|
| The sum of x and 5 | x + 5 |
| 7 less than y | y - 7 |
| The product of 3 and n | 3n |
| m divided by 4 | m/4 |
| Twice a number plus 3 | 2x + 3 |
| 5 more than twice x | 2x + 5 |
| The quotient of x and y, decreased by 2 | x/y - 2 |
⚠️ Watch Out!
"Less than" and "subtracted from" reverse the order!
• "7 less than y" = y - 7 (NOT 7 - y)
4Evaluating Expressions
Steps to Evaluate
- Substitute (replace) each variable with its given value
- Follow order of operations (PEMDAS)
- Simplify to get your answer
Example 1: Evaluate 3x + 2y when x = 4 and y = 5
Step 1: 3(4) + 2(5)
Step 2: 12 + 10
Answer: 22
Example 2: Evaluate x² - 3x + 1 when x = -2
Step 1: (-2)² - 3(-2) + 1
Step 2: 4 - (-6) + 1
Step 3: 4 + 6 + 1
Answer: 11
5Combining Like Terms
What Are Like Terms?
Terms with the same variable(s) raised to the same power.
✓ Like Terms
- 3x and 5x
- 2y² and -7y²
- 4 and -9 (constants)
✗ Unlike Terms
- 3x and 5y (different variables)
- 2x and 2x² (different powers)
- 4x and 4 (one has variable)
Combining Like Terms
Add or subtract the coefficients of like terms.
Example 1: Simplify 5x + 3x
= (5 + 3)x = 8x
Example 2: Simplify 7y - 2y + 4y
= (7 - 2 + 4)y = 9y
Example 3: Simplify 3x + 5y + 2x - y
= (3x + 2x) + (5y - y) = 5x + 4y