Factorising is like reverse multiplication - instead of expanding brackets,...
Mathematics9 views·Updated 12 Jul 2026·1 pageUnderstanding Algebra: A Student's Guide
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M@mcummins
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Factorising Techniques
The key to factorising is finding what's common between terms and pulling it out front. Start by looking for the highest common factor (HCF) of all the numbers and variables.
For simple expressions like 4x + 12, find the HCF of 4 and 12, which is 4. Then factor out: 4. With variables involved, like 3x² + 6x, you factor out both numbers and variables: 3x.
When you've got multiple variables like 6x²y + 3xy, look for the HCF of everything. Here it's 3xy, giving you 3xy. Always check your answer by expanding it back out.
Quick Check: After factorising, multiply your brackets back out to make sure you get the original expression!
The difference of two squares is a special pattern: x² - y² = x - y$$x + y. So 4x² - 9 becomes 2x - 3$$2x + 3 because 4x² = (2x)² and 9 = 3².
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Mathematics9 views·Updated 12 Jul 2026·1 pageUnderstanding Algebra: A Student's Guide
M
M@mcummins
Factorising is like reverse multiplication - instead of expanding brackets, you're putting expressions back into brackets. It's a crucial skill for solving equations and simplifying algebraic expressions that'll come up constantly in your Leaving Cert maths.
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Factorising Techniques
The key to factorising is finding what's common between terms and pulling it out front. Start by looking for the highest common factor (HCF) of all the numbers and variables.
For simple expressions like 4x + 12, find the HCF of 4 and 12, which is 4. Then factor out: 4. With variables involved, like 3x² + 6x, you factor out both numbers and variables: 3x.
When you've got multiple variables like 6x²y + 3xy, look for the HCF of everything. Here it's 3xy, giving you 3xy. Always check your answer by expanding it back out.
Quick Check: After factorising, multiply your brackets back out to make sure you get the original expression!
The difference of two squares is a special pattern: x² - y² = x - y$$x + y. So 4x² - 9 becomes 2x - 3$$2x + 3 because 4x² = (2x)² and 9 = 3².
We thought you’d never ask...
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
You can download the app in the Google Play Store and in the 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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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.
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