Factorising
Factorising is the reverse of expanding and writes an expression as a product of factors.
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Play with the controls to see the idea in action.
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Factorising is the reverse of expanding and writes an expression as a product of factors.
- Take out the highest common factor first
- Look for difference of two squares
- Check by expanding again
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Factorising?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Factorising. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.
Check that you can explain Factorising in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Factorising gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Factorising in detail
Factorising writes an expression as a product, the reverse of expanding. The first step is to take out the highest common factor: 6x + 9 = 3(2x + 3). A quadratic such as x² + 7x + 12 factorises into two brackets, (x + 3)(x + 4), by finding two numbers that multiply to 12 and add to 7.
Special cases include the difference of two squares, x² − 9 = (x − 3)(x + 3). Factorising helps solve quadratic equations, simplify algebraic fractions and understand graphs. You can always check by expanding your answer.
How the interactive helps you understand Factorising
Click a step, or use the Previous and Next buttons, to move through the sequence one stage at a time. Auto-play moves on for you.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Factorising.
Real-life uses and examples
- Use Factorising when comparing prices, discounts or recipe quantities in everyday life.
- Explain Factorising to a friend with a simple picture, such as a row of tiles or a bag of sweets.
- Spot Factorising in exam questions, where it often sits inside a short word problem.
Common mistakes to avoid
- Forgetting units, signs or brackets when you apply Factorising.
- Memorising the steps for Factorising without checking why they work.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Factorising
What is Factorising?
Factorising is the reverse of expanding and writes an expression as a product of factors.
What are the most important points about Factorising?
The main points are: Take out the highest common factor first; Look for difference of two squares; Check by expanding again.
Why is Factorising useful?
Understanding Factorising gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Factorising?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Factorising?
Related topics in Mathematics include Rearranging Formulae, The Quadratic Formula, Inequalities.