GCSE-ready- Home
- Lessons
- GCSE & IGCSE Mathematics
- Expanding and factorising
Expanding and factorising
Expanding removes brackets. Factorising puts them back. They are the same move in opposite directions.
Expanding a single bracket
Multiply everything inside by the term outside.
3(x + 4) = 3x + 12
Watch the signs: −2(x − 5) = −2x + 10
3(x + 4) = 3x + 12
Watch the signs: −2(x − 5) = −2x + 10
Factorising
Find the highest common factor of every term and take it outside.
6x + 15 = 3(2x + 5)
8x2 + 12x = 4x(2x + 3)
Check by expanding your answer.
6x + 15 = 3(2x + 5)
8x2 + 12x = 4x(2x + 3)
Check by expanding your answer.
Double brackets
Every term in the first bracket multiplies every term in the second. A grid keeps it tidy.
(x + 3)(x + 5) = x2 + 5x + 3x + 15 = x2 + 8x + 15
(x + 3)(x + 5) = x2 + 5x + 3x + 15 = x2 + 8x + 15
Expand and simplify 3(2x + 1) − 2(x − 4)
- 3(2x + 1) = 6x + 3
- −2(x − 4) = −2x + 8 (negative times negative is positive)
- Collect: 6x − 2x + 3 + 8 = 4x + 11
Answer: 4x + 11
Expand: multiply every term inside by the term outside. Factorise: take out the highest common factor. Double brackets: every term times every term.
The interactive lesson includes the diagrams for this topic.
Check you have got it
Answer 7 quick questions with instant marking. If you get one wrong, GCSE-ready shows you why and gives you another go. It is free, and you do not need an account.