Algebraic Expressions

Algebraic Expressions Explained

An algebraic expression is a mathematical phrase that contains variables (letters), numbers, and operations. Variables represent unknown quantities that we can work with mathematically.

Components of Algebraic Expressions

• Variables: Letters (x, y, a, b) representing unknown values
• Coefficients: Numbers multiplying the variables (e.g., in 3x, 3 is the coefficient)
• Constants: Numbers without variables
• Terms: Parts separated by + or - signs
• Operators: +, −, ×, ÷

Types of Expressions

Monomial: Single term. Example: 5x, 3ab, 7

Binomial: Two terms. Example: x + 2, 3x − 5y

Trinomial: Three terms. Example: x² + 3x + 2

Polynomial: Multiple terms. Example: x⁴ + 2x³ − x² + 5

Simplifying Expressions

Combine like terms (terms with the same variable raised to the same power).

Example: Simplify 3x + 5 + 2x − 3

Step 1: Group like terms: (3x + 2x) + (5 − 3)

Step 2: Combine: 5x + 2

Evaluating Expressions

Replace variables with given values and calculate.

Example: Evaluate 2x + 3 when x = 5

Substitute: 2(5) + 3 = 10 + 3 = 13

Operations on Expressions

Addition: (3x + 2) + (x + 5) = 4x + 7

Subtraction: (3x + 2) − (x + 5) = 2x − 3

Multiplication: 2x(3x + 4) = 6x² + 8x