Take out the highest common factor so the expression becomes a term times a bracket, and check by expanding.
What you will learn
- Find the highest common factor of terms
- Factorise fully into one bracket
- Check a factorisation by expanding
Expanding backwards
Factorising undoes expanding: it writes an expression as a product.
Find the highest common factor of all the terms and write it outside the bracket.
- 6x² + 9x
- HCF of 6 and 9 is 3; both terms have an x
- = 3x(2x + 3)
- check: 3x × 2x = 6x², 3x × 3 = 9x
For letter terms, the HCF takes the lowest power of each letter in every term: the HCF of 10a⁵ and 15a² is 5a². With three terms, the HCF must divide all three: 6x² − 9x + 12 = 3(2x² − 3x + 4).
"Factorise fully" means nothing common is left inside: 2x(3x + 4.5) is not allowed, and 3(2x² + 3x) still has x in both terms.
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- Expanding backwards
- With two letters
- Try it: Let the solver factorise
7 practice questions, marked as you go; about 20 minutes in all.
Key terms
Factorising, Highest common factor
In this unit: Algebraic expressions
The language of algebra: writing and substituting into expressions, simplifying, expanding brackets, factorising, and telling expressions, equations, formulae and identities apart.
- Writing and using algebra
- Simplifying
- Expanding brackets
- Factorising into one bracket
- Expressions, equations, formulae and identities