What Is the Algebraic Expressions?(With Examples)

An algebraic expression is a mathematical phrase that contains numbers, variables (letters representing unknown values), and operations (+, -, ×, ÷). Unlike equations, expressions don't have an equals sign. Examples: 3x + 5, 2a² - 4b, 7y.

Grades 6-7Key Stage 3 (Year 7-9)Årskurs 6-7Klasse 6-7

📖Definition

An algebraic expression is a mathematical phrase that contains numbers, variables (letters representing unknown values), and operations (+, -, ×, ÷). Unlike equations, expressions don't have an equals sign. Examples: 3x + 5, 2a² - 4b, 7y.

📐Formula

Examples: 3x + 5, 2a² - 4b + 7

In 3x + 5: 3x and 5 are terms, 3 is the coefficient of x, x is the variable, and 5 is a constant. Terms are separated by + or - signs.

📝Step-by-Step Guide

1

Identify the Parts

Find the terms, coefficients, variables, and constants in the expression.

2

Combine Like Terms

Add or subtract terms that have the same variable raised to the same power.

3x + 5x = 8x; 2x² + 3x² = 5x²
3

Distribute When Needed

Multiply a term outside parentheses by each term inside.

2(3x + 4) = 6x + 8
4

Evaluate the Expression

Substitute given values for variables and calculate the result.

If x = 3, then 2x + 7 = 2(3) + 7 = 13

⚠️Common Mistakes to Avoid

  • Combining unlike terms (3x + 2y ≠ 5xy)
  • Forgetting to distribute to all terms in parentheses
  • Confusing expressions with equations
  • Incorrectly handling negative signs when distributing
  • Adding exponents when combining like terms

✏️Practice Problems

Easy

Simplify 4x + 3x

Answer: 7x

Medium

Simplify 3(2x - 4) + 5x

Answer: 11x - 12

Hard

Evaluate 2x² - 3x + 5 when x = -2

Answer: 19

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Worked Examples

Curriculum Alignment

CommonCore (6.EE.A.2)KS3KMK