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Maths
29 Nov 2025
664
3 pages
StudyWfb @fb_emmf
Factorising is a key algebraic skill that helps you simplify expressions by putting terms into brackets. This method... Show more
Factorising means putting expressions into brackets to simplify them. The first step is deciding how many brackets you need - one bracket if terms share a common factor, or two brackets if they don't.
Look for common factors between terms. For example, in 10x² + 15xy, both terms share a factor of 5, so we need just one bracket. We place the common factor (5) outside the bracket like this 5( ).
Next, determine what goes inside the bracket by dividing each term by the common factor. For 10x²÷5 = 2x and 15xy÷5 = 3y, our answer becomes 5. Always check your answer by expanding the brackets to ensure you get the original expression.
Remember Factorising is like reverse-expanding brackets. If you can spot what's common between terms, you're halfway there!
When factorising expressions like x² + 9x + 20 that have no common factor across all terms, we need two brackets. These quadratic expressions typically follow the pattern ax² + bx + c.
Start by finding the factor pairs of the last number (c). For 20, the factor pairs are 1×20, 2×10, and 4×5. We need to find which pair adds up to the middle coefficient (9). Since 4+5=9, we'll use these numbers.
Write out your brackets as (x )(x ) because multiplying these gives us x². Then insert the factors . To check, multiply these brackets - you should get x² + 9x + 20.
Pro tip When factorising quadratics, always look for the factor pair that both multiplies to give the last term AND adds to give the middle coefficient.
After identifying your factors, place them in brackets with the x-terms. For example, with x² + 9x + 20, our final answer is . You can verify this works because 4×5=20 and 4x+5x=9x.
When factorising expressions with common factors first, like 9x² + 6x, identify what's common to all terms (in this case 3x) and factor it out 3x. Always check your work by expanding to confirm you get the original expression.
Practice makes perfect with factorising. Try working through examples of increasing difficulty to build your confidence. You'll soon find yourself spotting patterns quickly!
Quick check After factorising, always expand your brackets to make sure you get back to the original expression. If not, you've made a mistake somewhere.
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.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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Master the techniques for solving algebraic equations with one unknown variable. This guide covers addition, subtraction, multiplication, and division methods through clear examples and step-by-step explanations. Ideal for students tackling one-step and two-step equations in algebra.
MathsExplore essential Year 7 algebra concepts with this comprehensive guide. Dive into function machines, algebraic notation, sequences, and inverse operations. This resource includes key vocabulary, exemplar questions, and strategies for effective teaching and learning. Perfect for educators and students aiming to strengthen their understanding of algebraic principles.
MathsMaster the technique of expanding triple brackets with this concise guide tailored for GCSE students. This resource covers key concepts such as special products, the distributive property, and binomial expansion, providing clear examples and step-by-step explanations to enhance your understanding and problem-solving skills.
MathsThis comprehensive guide covers the techniques for expanding single, double, and triple brackets in mathematics. Learn methods such as FOIL and grid multiplication, and practice collecting like terms to simplify expressions. Ideal for Year 8/9 students looking to strengthen their algebra skills.
MathsExplore the BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction) rules for solving mathematical equations. This summary provides clear examples and step-by-step guidance on applying the order of operations effectively. Ideal for students looking to enhance their problem-solving skills in mathematics.
MathsExplore essential algebraic concepts including algebraic equations, manipulation, and expressions. This summary provides clear examples of expanding brackets, collecting like terms, and solving equations, making it a valuable resource for students looking to strengthen their understanding of algebra.
MathsApp Store
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 THE SCHOOLGPT. 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
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 THE SCHOOLGPT. 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
StudyWfb
@fb_emmf
Factorising is a key algebraic skill that helps you simplify expressions by putting terms into brackets. This method makes complex expressions easier to understand and solve. We'll look at different factorising techniques for various types of expressions.
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Join milions of students
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Factorising means putting expressions into brackets to simplify them. The first step is deciding how many brackets you need - one bracket if terms share a common factor, or two brackets if they don't.
Look for common factors between terms. For example, in 10x² + 15xy, both terms share a factor of 5, so we need just one bracket. We place the common factor (5) outside the bracket like this: 5( ).
Next, determine what goes inside the bracket by dividing each term by the common factor. For 10x²÷5 = 2x and 15xy÷5 = 3y, our answer becomes 5. Always check your answer by expanding the brackets to ensure you get the original expression.
Remember: Factorising is like reverse-expanding brackets. If you can spot what's common between terms, you're halfway there!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
When factorising expressions like x² + 9x + 20 that have no common factor across all terms, we need two brackets. These quadratic expressions typically follow the pattern ax² + bx + c.
Start by finding the factor pairs of the last number (c). For 20, the factor pairs are 1×20, 2×10, and 4×5. We need to find which pair adds up to the middle coefficient (9). Since 4+5=9, we'll use these numbers.
Write out your brackets as (x )(x ) because multiplying these gives us x². Then insert the factors: . To check, multiply these brackets - you should get x² + 9x + 20.
Pro tip: When factorising quadratics, always look for the factor pair that both multiplies to give the last term AND adds to give the middle coefficient.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
After identifying your factors, place them in brackets with the x-terms. For example, with x² + 9x + 20, our final answer is . You can verify this works because 4×5=20 and 4x+5x=9x.
When factorising expressions with common factors first, like 9x² + 6x, identify what's common to all terms (in this case 3x) and factor it out: 3x. Always check your work by expanding to confirm you get the original expression.
Practice makes perfect with factorising. Try working through examples of increasing difficulty to build your confidence. You'll soon find yourself spotting patterns quickly!
Quick check: After factorising, always expand your brackets to make sure you get back to the original expression. If not, you've made a mistake somewhere.
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.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
7
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Master the techniques for solving algebraic equations with one unknown variable. This guide covers addition, subtraction, multiplication, and division methods through clear examples and step-by-step explanations. Ideal for students tackling one-step and two-step equations in algebra.
MathsExplore essential Year 7 algebra concepts with this comprehensive guide. Dive into function machines, algebraic notation, sequences, and inverse operations. This resource includes key vocabulary, exemplar questions, and strategies for effective teaching and learning. Perfect for educators and students aiming to strengthen their understanding of algebraic principles.
MathsMaster the technique of expanding triple brackets with this concise guide tailored for GCSE students. This resource covers key concepts such as special products, the distributive property, and binomial expansion, providing clear examples and step-by-step explanations to enhance your understanding and problem-solving skills.
MathsThis comprehensive guide covers the techniques for expanding single, double, and triple brackets in mathematics. Learn methods such as FOIL and grid multiplication, and practice collecting like terms to simplify expressions. Ideal for Year 8/9 students looking to strengthen their algebra skills.
MathsExplore the BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction) rules for solving mathematical equations. This summary provides clear examples and step-by-step guidance on applying the order of operations effectively. Ideal for students looking to enhance their problem-solving skills in mathematics.
MathsExplore essential algebraic concepts including algebraic equations, manipulation, and expressions. This summary provides clear examples of expanding brackets, collecting like terms, and solving equations, making it a valuable resource for students looking to strengthen their understanding of algebra.
MathsApp Store
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 THE SCHOOLGPT. 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
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 THE SCHOOLGPT. 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
Algebra 1
Sociology