GCSE maths · Algebra
Expanding brackets and factorising
Revision notes for Foundation and Higher. Three ideas, each with a worked example, the reason for every line, and the trap to avoid.
Every worked example was checked by the code that marks Mathable’s tests.
1Multiply every pair of terms
Multiply each term in the first bracket by each term in the second, then collect like terms.
Think of it like
Think of a grid: each term in one bracket meets every term in the other, like a timetable.
Worked example
Expand and simplify (x + 6)(x − 5).
- multiply first terms
- multiply outer terms
- multiply inner terms
- multiply last terms
- Answercollect like terms
TrapIf you only multiply the first terms together, you miss three of the four products.
Explain it back
Why do you need four separate multiplications for two brackets?
Say it out loud in two or three sentences. Where you get stuck is what to revise.
2Pull out the HCF
Find the biggest number and letter that divide every term, then write it outside the bracket.
Think of it like
Think of the HCF as a common wrapper you can lift off every term, leaving the leftovers inside.
Worked example
Factorise fully 20x² − 12x.
- HCF of 20x² and 12x is 4xfind biggest shared factor
- Answerwrite factor outside brackets
TrapIf you only take out 2x instead of 4x, the bracket is not fully factorised.
Explain it back
Why must the HCF divide both terms exactly?
3Spot the difference of squares
If you see x squared minus a square number, it factors as two brackets, one plus one minus.
Think of it like
Two squares, one cut from a corner of the other, leave an L-shape that rearranges into a rectangle.
Worked example
Factorise x² − 64.
- write 64 as 8 squared
- Answerone bracket plus, one minus
TrapIf you write (x − 8)(x − 8), the middle terms don't cancel and it's wrong.
Explain it back
Why does one bracket need a plus and the other a minus?
Practise with Mathable
Practise expanding brackets with a tutor that checks every line
- ›Ten questions on expanding brackets, marked for you.
- ›It points at the first mistake in your working.
- ›One hint at a time, so you work out the fix yourself.
- ›Explain an idea back, and it tells you the one gap.
The free week needs a card. You won’t be charged if you cancel before the week ends.
