•

Updated Mar 15, 2026

•

2 pages

Fun with Expanding Brackets: Simple Steps & Cool Examples for Algebra Practice!

Ruby

@_fipd

Expanding brackets is a fundamental algebraic operation that involves multiplying... Show more

# math
Expanding brackets.
Example
5(x + 4) +3 (2x + 1)
=5x +20 + 6x + 3
=11x +23.

E xample 2
x(3x + 4)
=3x² + 4 x

Example 3
6x(-2 + 3)
=

Advanced Expanding Brackets Techniques

This page delves into more complex examples of expanding brackets, including scenarios with higher degree polynomials and multiple sets of brackets.

The first example demonstrates expanding brackets with a quadratic term:

$x + 2$ $x² + x + 3$ = x³ + 3x² + 5x + 6

Highlight: When expanding brackets with higher degree terms, be careful to correctly multiply the exponents.

The page then shows an example with two sets of brackets, each containing multiple terms:

$2x - 1$ $7x² + x - 5$ = 14x³ + 2x² - 10x - 7x² - x + 5 = 14x³ - 5x² - 11x + 5

This example illustrates the importance of methodically multiplying each term and carefully combining like terms.

Example: $3x + 1$ $x + 1$ + 2 $x² - 5$ = 3x² + 5x² + 4x - 9

This problem combines expanding brackets with additional operations, demonstrating how these skills are applied in more complex algebraic expressions.

The page concludes with two more examples:

$2x - 5$ $3x + 1$ = 6x² - 13x - 5

$x - 4$ $x² + x - 2$ = x³ + x² - 2x - 4x² - 4x + 8 = x³ - 3x² - 6x + 8

Vocabulary: Polynomial - An expression consisting of variables and coefficients, involving only addition, subtraction, and multiplication operations.

These final examples reinforce the techniques for expanding double brackets and handling more complex algebraic expressions.

Highlight: Practice is key to mastering the skill of expanding brackets. Use expanding brackets worksheets and expanding brackets examples for algebra practice to improve your proficiency.

Expanding Brackets: Basic to Advanced Examples

This page introduces the concept of expanding brackets in algebra, providing a range of examples from simple to complex. Expanding brackets is a crucial skill in algebra, used to simplify expressions and solve equations.

Definition: Expanding brackets means multiplying the term outside the brackets by each term inside, then combining like terms.

The page starts with a simple example:

5 $x + 4$ + 3 $2x + 1$ = 5x + 20 + 6x + 3 = 11x + 23

This example demonstrates the basic process of distributing the outside term to each term inside the brackets, then combining like terms.

Example: x $3x + 4$ = 3x² + 4x

This shows how to expand when the outside term is a variable.

The page then progresses to more complex examples, including expanding double brackets:

Example: $x + 2$ $x + 5$ = x² + 7x + 10

This illustrates the FOIL method (First, Outer, Inner, Last) for expanding double brackets, which is a key technique in expanding double brackets.

Highlight: When expanding double brackets, remember to multiply each term in the first bracket by each term in the second bracket.

The page also includes examples with negative terms:

6x(-2 + 3) = -12x + 18x = 6x

$-x + 6$ $3x - 5$ = -3x² + 23x - 30

These examples emphasize the importance of careful sign management when expanding brackets with negative terms.

Vocabulary: FOIL - A method for expanding double brackets, standing for First, Outer, Inner, Last.

We thought you’d never ask...

What is the Knowunity AI companion?

Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.

Where can I download the Knowunity app?

You can download the app from Google Play Store and Apple App Store.

Is Knowunity really free of charge?

That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.

Most popular content in Maths

Comprehensive Maths Concepts

Explore essential mathematical concepts including powers, geometry, statistics, and probability. This resource features 65 pages of detailed explanations, diagrams, and examples to enhance your understanding of topics such as right triangles, volume calculations, and data representation. Ideal for students seeking to strengthen their numeracy skills and grasp complex mathematical principles.

Maths

GCSE Maths (Higher) // Revision Guide

The only GCSE maths (higher) revision guide you need to get a grade 9! Contains every topic, each with all potential question types and their solutions.

Maths

Comprehensive Maths Concepts

Explore essential mathematical concepts including polynomial theorems, logarithmic properties, trigonometric functions, and integration techniques. This resource covers everything from solving inequalities to understanding exponential functions, providing a solid foundation for A-level mathematics. Ideal for students aiming for top grades.

Maths

Comprehensive Maths Concepts

Explore essential higher mathematics concepts including calculus, trigonometry, polynomials, and vector analysis. This summary covers key topics such as differentiation, integration, quadratic equations, and the properties of circles, providing a solid foundation for exam preparation. Ideal for students seeking a concise yet thorough review of advanced mathematical principles.

Maths

Comprehensive Pure Mathematics

Explore detailed notes on Pure Mathematics Year 1, covering essential topics such as simultaneous equations, differentiation, integration, trigonometric functions, and more. Perfect for A Level Edexcel students seeking a thorough understanding of mathematical concepts and techniques.

Maths

GCSE Higher Maths Essentials

Master key concepts in GCSE Higher Maths with this comprehensive summary covering geometry, algebra, probability, and circle theorems. Perfect for exam preparation, this resource includes essential formulas, angle facts, area calculations, and statistical measures to boost your understanding and performance. Ideal for students aiming for top grades.

Maths

AS Level Statistics Overview

Explore key concepts in AS Level Statistics, including hypothesis testing, binomial distribution, linear regression, and sampling methods. This summary covers essential statistical measures, significance levels, and data analysis techniques, providing a comprehensive guide for Year 1 applied maths students.

Maths

Edexcel Maths Practice Paper

Prepare for your Edexcel Maths exam with this comprehensive practice paper covering key topics such as powers of 10, statistical averages, geometric transformations, and algebraic equations. This resource includes a variety of question types to enhance your numeracy skills and exam readiness.

Maths

UK Weather Data Analysis

Explore the Edexcel large data set on UK weather, including daily mean temperatures, rainfall patterns, and wind speeds. This summary covers key statistics, comparisons between locations, and trends over time, making it essential for understanding weather systems and climate variations. Ideal for students studying descriptive statistics and data distribution.

Maths

Most popular content

An Inspector Calls: Character Insights

Explore in-depth analysis and key quotes for characters in J.B. Priestley's 'An Inspector Calls'. This resource covers Gerald Croft, Inspector Goole, Sheila Birling, Mrs. Birling, Eric Birling, and Eva Smith, focusing on themes of class, gender roles, and social responsibility. Ideal for students aiming for Grade 8 and above.

English Literature

Sociology of Education Overview

Explore comprehensive A-Level Sociology notes on the education system, covering key theories, policies, and sociological perspectives. This resource includes insights on marketisation, gender roles, cultural deprivation, and educational inequalities, providing a thorough understanding of how education shapes social stratification and individual achievement. Ideal for exam preparation and in-depth study.

Sociology

Comprehensive Crime & Deviance Overview

Explore an extensive revision of crime and deviance topics, including theories, types of crime, and the impact of media. This resource covers key concepts such as Marxism, functionalism, gender and crime, and the influence of globalization on criminal behavior. Ideal for students seeking a thorough understanding of criminology and its various theories. Type: Full Topic Revision.

Sociology

Sociology of Families: Comprehensive Revision

Dive into an extensive overview of family dynamics, perspectives, and patterns in sociology. This resource covers key concepts such as family diversity, gender roles, marriage, and the impact of social policies on family structures. Perfect for A-Level Sociology students preparing for Paper 2.

Sociology

WJEC Unit 4 Criminology

Criminology unit 4 detailed revision note

Criminology

aqa higher tier combined science - biology b1 : cell biology, paper 1

b1: cell biology - paper 1

Biology

Criminology: Crime & Punishment Overview

Comprehensive mindmaps covering key concepts in the Crime and Punishment topic for WJEC Criminology Unit 4. This resource includes detailed insights into the Criminal Justice System, crime prevention strategies, sentencing models, and the roles of various agencies. Ideal for A-Level revision, ensuring you grasp essential theories and legislative processes to excel in your exams.

Criminology

Macbeth: Guilt and Ambition

Explore the complex themes of guilt and ambition in Shakespeare's 'Macbeth'. This analysis covers key characters, including Macbeth and Lady Macbeth, their moral dilemmas, and the tragic consequences of their ambition. Ideal for students studying character motivations, thematic elements, and the psychological impact of power. Includes insights on the natural order, manipulation, and the descent into madness.

English Literature

AQA Biology: Key Concepts

Explore essential AQA Biology topics including Photosynthesis, Respiration, Homeostasis, Genetics, and Ecology. This comprehensive knowledge organizer covers key concepts such as energy transfer, hormonal control, and genetic variation, providing a solid foundation for your studies. Ideal for exam preparation and understanding biological processes.

Biology

Can't find what you're looking for? Explore other subjects.

Students love us — and so will you.

4.6/5

App Store

4.7/5

Google Play

The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

Best app on earth! no words because it’s too good

Thomas R

iOS user

Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.

Basil

Android user

This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.

Rohan U

Android user

I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.

Xander S

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now

Paul T

iOS user

Stefan S

iOS user

Samantha Klich

Android user

Anna

iOS user

Best app on earth! no words because it’s too good

Thomas R

iOS user

Basil

Android user

David K

iOS user

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

Rohan U

Android user

Xander S

iOS user

Elisha

iOS user

Paul T

iOS user

Maths

•

Updated Mar 15, 2026

•

2 pages

Fun with Expanding Brackets: Simple Steps & Cool Examples for Algebra Practice!

Ruby

@_fipd

Expanding brackets is a fundamental algebraic operation that involves multiplying terms inside parentheses by terms outside. This process is crucial in simplifying expressions and solving equations. Expanding bracketsrequires careful attention to the rules of multiplication and distribution, especially when... Show more

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

Advanced Expanding Brackets Techniques

This page delves into more complex examples of expanding brackets, including scenarios with higher degree polynomials and multiple sets of brackets.

The first example demonstrates expanding brackets with a quadratic term:

$x + 2$ $x² + x + 3$ = x³ + 3x² + 5x + 6

Highlight: When expanding brackets with higher degree terms, be careful to correctly multiply the exponents.

The page then shows an example with two sets of brackets, each containing multiple terms:

$2x - 1$ $7x² + x - 5$ = 14x³ + 2x² - 10x - 7x² - x + 5 = 14x³ - 5x² - 11x + 5

This example illustrates the importance of methodically multiplying each term and carefully combining like terms.

Example: $3x + 1$ $x + 1$ + 2 $x² - 5$ = 3x² + 5x² + 4x - 9

This problem combines expanding brackets with additional operations, demonstrating how these skills are applied in more complex algebraic expressions.

The page concludes with two more examples:

$2x - 5$ $3x + 1$ = 6x² - 13x - 5

$x - 4$ $x² + x - 2$ = x³ + x² - 2x - 4x² - 4x + 8 = x³ - 3x² - 6x + 8

Vocabulary: Polynomial - An expression consisting of variables and coefficients, involving only addition, subtraction, and multiplication operations.

These final examples reinforce the techniques for expanding double brackets and handling more complex algebraic expressions.

Highlight: Practice is key to mastering the skill of expanding brackets. Use expanding brackets worksheets and expanding brackets examples for algebra practice to improve your proficiency.

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

Expanding Brackets: Basic to Advanced Examples

Definition: Expanding brackets means multiplying the term outside the brackets by each term inside, then combining like terms.

The page starts with a simple example:

5 $x + 4$ + 3 $2x + 1$ = 5x + 20 + 6x + 3 = 11x + 23

This example demonstrates the basic process of distributing the outside term to each term inside the brackets, then combining like terms.

Example: x $3x + 4$ = 3x² + 4x

This shows how to expand when the outside term is a variable.

The page then progresses to more complex examples, including expanding double brackets:

Example: $x + 2$ $x + 5$ = x² + 7x + 10

This illustrates the FOIL method (First, Outer, Inner, Last) for expanding double brackets, which is a key technique in expanding double brackets.

Highlight: When expanding double brackets, remember to multiply each term in the first bracket by each term in the second bracket.

The page also includes examples with negative terms:

6x(-2 + 3) = -12x + 18x = 6x

$-x + 6$ $3x - 5$ = -3x² + 23x - 30

These examples emphasize the importance of careful sign management when expanding brackets with negative terms.

Vocabulary: FOIL - A method for expanding double brackets, standing for First, Outer, Inner, Last.