Algebraic Expressions

What is an Algebraic Expression?

An algebraic expression contains numbers, variables (letters representing unknown values), and operations. Unlike equations, expressions do not have an equals sign.

Examples: 3x + 5, 2a² - b, 4(x + 3)

Key Vocabulary

• Term: a single number, variable, or product: 3x, -2y², 7
• Coefficient: the number in front of a variable: in 5x, the coefficient is 5
• Constant: a fixed number with no variable: in 3x + 7, the constant is 7
• Like terms: terms with the same variable and power: 3x and 5x are like terms

Simplifying Expressions

Collect like terms by adding or subtracting their coefficients:

• 4x + 3y + 2x - y = (4+2)x + (3-1)y = 6x + 2y

You cannot simplify unlike terms (3x + 5y cannot be simplified further).

Expanding Brackets

Multiply every term inside the bracket by the term outside:

• 3(2x + 5) = 3×2x + 3×5 = 6x + 15

Substitution

Replace variables with given values to evaluate an expression:

• If x = 3: 2x² - x + 4 = 2(9) - 3 + 4 = 18 - 3 + 4 = 19