Factorising Expressions
Factorise algebraic expressions by taking out common factors — identify the highest common factor of all terms and write the expression as a product, e.g., 6x + 9 = 3(2x + 3)
What a learner can do afterwards
- Identify the highest common factor of all terms in an expression
- Write the factorised form as a product of the HCF and a bracket
- Check factorisation by expanding the brackets back out
The lesson
You already know how to expand brackets, turning something like 3(2x + 3) into 6x + 9. Factorising goes the other way. You start with 6x + 9 and rewrite it as 3(2x + 3).
To factorise, first find the highest common factor, or HCF, of every term. The HCF is the biggest number that divides evenly into all of them. For 6x + 9, that number is 3.
Look at 6x + 9. The terms are 6x and 9. The biggest number that divides both 6 and 9 is 3. Divide each term by 3: 6x divided by 3 is 2x, and 9 divided by 3 is 3. Write the HCF outside a bracket with the results inside: 3(2x + 3).
Try 10x - 15. The highest common factor of 10 and 15 is 5. Dividing each term by 5 gives 2x and 3, so the factorised form is 5(2x - 3).
Always check your answer by expanding the brackets back out. If 3(2x + 3) really equals 6x + 9, your factorising is correct.
Find the biggest number that divides every term, write it outside a bracket, then check by expanding back out.
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