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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

📐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

Identify the Parts

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

Combine Like Terms

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

3x + 5x = 8x; 2x² + 3x² = 5x²

Distribute When Needed

Multiply a term outside parentheses by each term inside.

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

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

Simplify Algebraic Expressionsmedium

Linear Equations Polynomials Factoring Order of Operations

Curriculum Alignment

CommonCore (6.EE.A.2)KS3KMK

Classroom assessment context

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