Variable Expression Definition, Types & Examples
Lesson Overview
- What Are Variables and Expressions in Math?
- Types of Variable Expressions in Math
- Difference Between An Equation And An Expression
- Solved Examples on Variable Expressions
Mathematics needs tools to represent the unknown and ever-changing. This is where variables and expressions come into play. They are essential for expressing mathematical ideas clearly and concisely. Variables act as labels for quantities that we don't know or that can change.
Expressions combine these variables with numbers and operations, creating a powerful shorthand for calculations. With variables and expressions, we can describe relationships, solve problems, and make predictions.
What Are Variables and Expressions in Math?
A variable is a symbol, typically an alphabetic character, that represents a numerical value. This value may be unknown or may change within the context of a given problem.
For example, in the equation x + 5 = 7, x is a variable representing the unknown value 2.
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An expression is a mathematical phrase that combines numbers, variables, and operators (such as +, -, ×, ÷) to represent a value or relationship.
For example, the following is an expression which combines numbers, variables and an operator.
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Parts of An Expression
An expression has different parts that work together:
- Constants are fixed numerical values that don't change.
- Variables: These are symbols (usually letters) representing unknown or changeable values.
- Coefficients: These are numbers that multiply variables.
- Terms: A term is a single number, a variable, or the product of numbers and variables.
For example, in the expression: 4y² - 3y + 7
- Constants: 7
- Variables: y
- Coefficients: 4 (coefficient of y²), -3 (coefficient of y)
- Operators: - (subtraction), + (addition)
- Terms: 4y², -3y, 7
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Types of Variable Expressions in Math
There are 4 main types of variable expressions in mathematics.
| Type | Meaning | Examples |
| Monomial | An expression with a single term. | 3x |
| Binomial | An expression with two terms. | 2x + 5y |
| Trinomial | An expression with three terms. | x² + 3x - 7 |
| Polynomial | An expression with one or more terms. This is a general term that includes monomials, binomials, trinomials, and expressions with even more terms. | 4x³ - 2x² + 5x - 1 |
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Difference Between An Equation And An Expression
Equations and expressions are fundamental components of algebra, but they serve distinct purposes.
| Feature | Expression | Equation |
| Definition | A mathematical phrase combining numbers, variables, and operations. | A mathematical statement that asserts the equality of two expressions. |
| Equal Sign | Does not contain an equal sign (=). | Contains an equal sign (=). |
| Purpose | Represents a value. | Shows a relationship between two values. |
| Solution | Can be simplified or evaluated. | Can be solved for the value(s) of the variable(s). |
| Example | 4x + 7 | 4x + 7 = 15 |
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Solved Examples on Variable Expressions
Example 1: Evaluate 2x - 5 when x = 4
- Substitute 4 for x: 2(4) - 5
- Simplify: 8 - 5 = 3
Example 2: Simplify 3a + 2b - a + 5b
- Combine like terms: (3a - a) + (2b + 5b)
- Simplify: 2a + 7b
Example 3: Write an expression for "twice a number increased by seven."
- Let "n" represent the number.
- Translate: 2n + 7
Example 4: Evaluate x^2 - 3y when x = -2 and y = 5.
- Simplify (-2)^2 - 3(5)
- 4 - 15 = -11
Example 5: Simplify 4x^3 + 2x^3 - x^2.
- Simplify (4x^3 + 2x^3) - x^2
- 6x^3 - x^2
Example 6: A taxi charges $3 plus $2 per mile. Write an expression for the cost of a ride.
- Let "m" represent the number of miles.
- Write the expression: 3 + 2m
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