IGCSE Simplifying Algebraic Expressions: Complete Guide for Cambridge IGCSE Mathematics

IGCSE simplifying algebraic expressions is a fundamental algebra skill in Cambridge IGCSE Mathematics that appears in both Paper 2 and Paper 4. Mastering collecting like terms, expanding brackets, and simplifying expressions is essential for solving algebraic problems efficiently.

This comprehensive IGCSE simplifying algebraic expressions guide covers everything you need to know, including collecting like terms, expanding brackets, factorizing, worked examples, common exam questions, and expert tips from Tutopiya’s IGCSE maths tutors. We’ll also show you how to avoid the most common mistakes that cost students valuable marks.

🎯 What you’ll learn: By the end of this guide, you’ll know how to collect like terms, expand and simplify brackets, factorize expressions, and apply these skills to solve problems in IGCSE exams.

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Why IGCSE Simplifying Algebraic Expressions Matters

IGCSE simplifying algebraic expressions is an essential algebra skill. Here’s why it’s so important:

• High frequency topic: Simplification questions appear regularly in IGCSE maths papers
• Foundation skill: Essential for solving equations and word problems
• Exam weight: Typically worth 3-6 marks per paper
• Real-world applications: Used in all areas of mathematics and science
• Problem-solving skills: Develops algebraic thinking and manipulation abilities

Key insight from examiners: Students often make errors with signs, forget to collect all like terms, or make mistakes when expanding brackets. This guide will help you master these systematically.

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Understanding Simplifying Algebraic Expressions

Simplifying algebraic expressions means rewriting expressions in their simplest form by:

• Collecting like terms
• Expanding and simplifying brackets
• Combining constants

Example: 3x + 2x - 5 + 7 simplifies to 5x + 2

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Collecting Like Terms

Like terms are terms that have the same variables raised to the same powers.

Examples of Like Terms

• 3x and 5x (both have x)
• 2y² and -7y² (both have y²)
• 4 and -3 (both are constants)

Examples of Unlike Terms

• 3x and 3y (different variables)
• 2x and 2x² (different powers)

Worked Examples

Example 1: Simplify 5x + 3x - 2x

Solution: 5x + 3x - 2x = (5 + 3 - 2)x = 6x

Answer: 6x

Example 2: Simplify 4a + 3b - 2a + 5b

Solution: Collect like terms:

• Terms with a: 4a - 2a = 2a
• Terms with b: 3b + 5b = 8b

4a + 3b - 2a + 5b = 2a + 8b

Answer: 2a + 8b

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Expanding Brackets

Expanding brackets means multiplying out expressions within brackets.

Single Brackets

Use the distributive property: a(b + c) = ab + ac

Example 1: Expand 3(x + 4)

Solution: 3(x + 4) = 3(x) + 3(4) = 3x + 12

Answer: 3x + 12

Example 2: Expand -2(x - 5)

Solution: -2(x - 5) = -2(x) + (-2)(-5) = -2x + 10

Answer: -2x + 10

Double Brackets

Use FOIL method: First, Outside, Inside, Last

Example 3: Expand (x + 3)(x + 5)

Solution:

• First: x × x = x²
• Outside: x × 5 = 5x
• Inside: 3 × x = 3x
• Last: 3 × 5 = 15

(x + 3)(x + 5) = x² + 5x + 3x + 15 = x² + 8x + 15

Answer: x² + 8x + 15

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Step-by-Step Method for Simplifying

1. Expand brackets - Multiply out all brackets first
2. Collect like terms - Group terms with the same variables
3. Simplify - Combine like terms and constants
4. Check - Verify your answer makes sense

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Worked Examples

Example 1: Basic Simplification

Simplify 2x + 5 + 3x - 7

Solution: Collect like terms:

• Terms with x: 2x + 3x = 5x
• Constants: 5 - 7 = -2

2x + 5 + 3x - 7 = 5x - 2

Answer: 5x - 2

Example 2: With Brackets

Simplify 3(x + 2) + 4(x - 1)

Solution: Step 1: Expand brackets 3(x + 2) = 3x + 6 4(x - 1) = 4x - 4

Step 2: Collect like terms 3x + 6 + 4x - 4 = 7x + 2

Answer: 7x + 2

Example 3: Complex Expression

Simplify 2(3x - 4) - 3(x + 2)

Solution: Step 1: Expand brackets 2(3x - 4) = 6x - 8 -3(x + 2) = -3x - 6

Step 2: Combine 6x - 8 - 3x - 6 = 3x - 14

Answer: 3x - 14

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Common Examiner Traps

• Sign errors - Watch positive/negative signs carefully, especially with brackets
• Forgetting to expand - Always expand brackets before collecting like terms
• Incomplete collection - Make sure you collect ALL like terms
• Double brackets - Use FOIL method correctly for (a+b)(c+d)
• Negative signs - Be careful when expanding expressions with negative coefficients

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IGCSE Simplifying Algebraic Expressions Practice Questions

Question 1

Simplify 5x + 3 - 2x + 7

Solution: Collect like terms:

• Terms with x: 5x - 2x = 3x
• Constants: 3 + 7 = 10

5x + 3 - 2x + 7 = 3x + 10

Answer: 3x + 10

Question 2

Simplify 4(2x + 3) - 2(x - 1)

Solution: Expand: 8x + 12 - 2x + 2 Simplify: 6x + 14

Answer: 6x + 14

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Frequently Asked Questions About IGCSE Simplifying Algebraic Expressions

What are like terms?

Like terms are terms that have the same variables raised to the same powers. For example, 3x and 5x are like terms.

How do I collect like terms?

Add or subtract the coefficients of like terms while keeping the variable part the same.

How do I expand brackets?

Use the distributive property: multiply each term inside the bracket by the term outside.

What is the FOIL method?

FOIL stands for First, Outside, Inside, Last - a method for expanding double brackets like (a+b)(c+d).

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Related IGCSE Maths Resources

Strengthen your IGCSE Mathematics preparation with these comprehensive guides:

• IGCSE Substitution: Complete Guide - Master algebraic substitution
• IGCSE Factorisation: Complete Guide - Master factorizing expressions
• IGCSE Maths Revision Notes, Syllabus and Preparation Tips - Complete syllabus overview, topic breakdown, and revision strategies
• IGCSE Past Papers Guide - Access free IGCSE past papers and exam resources

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