GCSE Maths · Topic guide
Expanding and Factorising
Expanding means multiplying out brackets so there are no brackets left. Factorising is the reverse process: writing an expression as a product using brackets, by taking out the highest common factor.
Before you start
Make sure you're comfortable with these topics first:
Method
- To expand a single bracket, multiply everything inside the bracket by the term outside it.
- To expand two brackets, multiply every term in the first bracket by every term in the second bracket, then simplify by collecting like terms.
- To factorise, find the highest common factor (HCF) of every term in the expression.
- Write the HCF outside a bracket, and inside the bracket write what each term becomes when divided by the HCF.
- Check your factorising by expanding the bracket back out - you should get the original expression.
Worked example
Expand and simplify (x + 5)(x - 3), then factorise 6x^2 + 9x.
- Expand (x + 5)(x - 3) by multiplying every term in the first bracket by every term in the second: x*x + x*(-3) + 5*x + 5*(-3).
- This gives x^2 - 3x + 5x - 15.
- Collect the like terms -3x and 5x to get 2x: x^2 + 2x - 15.
- For 6x^2 + 9x, the highest common factor of 6x^2 and 9x is 3x.
- Divide each term by 3x: 6x^2 divided by 3x = 2x, and 9x divided by 3x = 3.
- So 6x^2 + 9x factorises to 3x(2x + 3).
Practice questions
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Exam-style questions
Written in the style of a GCSE exam paper, with a full mark scheme.
Q1[2 marks]
Expand and simplify (2x + 3)(x - 5).
Q2[2 marks]
Factorise fully 12x^2y - 18xy^2.
Next topics
Quadratic FormulaExpanding and Factorising Quadratics
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