GCSE maths revision


Factorising linear expressions


To factorise an expression means to 'put into brackets' by taking out common factors. When factorising, always take the largest factors possible out of the expression.

Factorising is the opposite of expanding or multiplying out expressions. Make sure you are comfortable with these revision notes before you attempt factorising!

Examples of how to factorise linear expressions

Example 1 - Factorising simple linear expressions

a) Factorise: \(3x + 9\).

Notice 3 is both a factor of \(3x\) and \(9\). We can factorise the expression by taking the \(3\) outside of the brackets.

\(3x + 9 = 3(x + 3)\).

b) Factorise: \(3a - a^2\).

This time the \(a\) is common to both terms.

\(3a - a^2 = a(3 - a)\).

c) Factorise: \(21a - 14b + 28c\).

When dealing with longer expressions, you need to find a factor common to all of the terms. In this case 7.

\(21a - 14b + 28c = 7(3a - 2b + 4c)\).

Example 2 - Factorising a linear expression fully

a) Factorise: \(18a + 24b)\).

To factorise an expression fully, you need to take out the largest factor out possible.

For example, we could take a \(2\) out to get \(2(9a + 12b)\). This is not factorised fully since \(9a\) and \(12b\) still share a common factor of \(3\). The largest factor we can take out is \(6\).

\(18a + 24b = 6(3a + 4b)\).

b) Factorise: \(4x + 10x^2\).

This time there are two common factors, \(2\) goes into both \(4\) and \(10\) so this is one factor. Also an \(x\) can be taken out.

\(4x + 10x^2 = 2x(2 + 5x)\).

Worksheets to practise factorising linear and quadratic expressions

Try this worksheet to practise your skills.