Factorisation — Common Factor & Grouping explained through a friendly whiteboard conversation, examples, visuals, and practice for school students.
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Notes
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Formulae
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Examples
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Practice
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Factorisation means writing an expression as a product of factors.
It is the reverse of expansion.
Common factor and grouping methods help students simplify expressions and prepare for equations.
A factor is something that multiplies with another factor to make a product.
In algebra, a common factor may include numbers, variables, or both.
The highest common factor, or HCF, is the greatest factor shared by all terms.
Grouping is useful when all terms do not have one common factor at first. Terms are grouped so each group has a common factor.
A correct factorisation can be checked by expanding it back.
Meaning: Factorisation rewrites a sum or difference as a product.
Definition: Factorisation is the process of expressing an algebraic expression as a product of factors.
6 can be written as 3(2).
Meaning: A common factor divides every term.
Definition: A common factor is a factor present in all terms of an expression.
In 8, the common factor is 4.
Meaning: The HCF is the largest common factor.
Definition: The HCF of algebraic terms is the greatest factor common to all terms.
The HCF of 12 and 18x is 6x.
Meaning: Grouping splits terms into pairs or groups that can be factorised.
Definition: Factorisation by grouping uses common factors in groups to create a common bracket.
a().
Easy
Question: Factorise 10.
Medium
Question: Factorise 12a.
Exam-level
Question: Factorise ay.
Taking a factor that is not common to every term
Why it happens: The largest visible factor is chosen too quickly.
Correct approach: Check every term before taking a common factor.
Forgetting the remaining bracket term
Why it happens: Only the outside factor is written.
Correct approach: Divide each term by the common factor to fill the bracket.
Grouping terms so brackets do not match
Why it happens: Terms are paired without a plan.
Correct approach: Rearrange or regroup so a common bracket appears.
How do I check factorisation?
Expand your answer. It should return to the original expression.
What if the common factor is negative?
You may take a negative common factor if it makes the bracket neater.
Can grouping have more than one correct order?
Yes, but the final factorised form should be equivalent.
Practise the same concept from this article. Your student profile may guide entitlement and follop recommendations, but it does not replace this concept.