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Factorising GCSE Maths

Factorising is the reverse of expanding brackets. Instead of removing a bracket, you are putting one back in.

This topic appears often in GCSE Maths and is important for simplifying expressions, solving equations, and working with quadratics.

What Does Factorising Mean?

Factorising means writing an expression as a product of brackets or simpler terms.

For example:

3x + 12

can be factorised by taking out the common factor of 3:

3x + 12 = 3(x + 4)

How to Factorise by Taking Out a Common Factor

Example:

5y + 15

Step 1: Look for the biggest factor that goes into both terms.

Both 5y and 15 can be divided by 5.

Step 2: Put 5 outside the bracket.

Step 3: Work out what stays inside the bracket.

5y + 15 = 5(y + 3)

Example with Variables

6x² + 9x

The biggest common factor is 3x.

So:

6x² + 9x = 3x(2x + 3)

How to Check Your Answer

A very good habit is to expand your brackets again to check.

For example:

3x(2x + 3)

expands to:

6x² + 9x

so the factorising is correct.

Factorising Simple Quadratics

Higher-tier students may also need to factorise expressions such as:

x² + 7x + 12

We need two numbers that:

  • multiply to make 12
  • add to make 7

Those numbers are 3 and 4.

So:

x² + 7x + 12 = (x + 3)(x + 4)

Common Mistakes

  • taking out a factor that is not common to every term
  • forgetting that variables can also be common factors
  • sign mistakes inside the bracket
  • not checking by expanding again

Quick Practice Questions

  1. 4x + 20
  2. 7a - 21
  3. 10y + 15
  4. 8x² + 12x
  5. x² + 9x + 20

Answers

  1. 4(x + 5)
  2. 7(a - 3)
  3. 5(2y + 3)
  4. 4x(2x + 3)
  5. (x + 4)(x + 5)

Final Tip

Factorising gets much easier when you always ask: what is common to all the terms? Then check your answer by expanding.