How to factorise expressions

Factorising - Expanding Brackets

This section shows you how to factorise and includes examples, sample questions and videos.

Brackets should be expanded in the following ways:

For an expression of the form a(b + c), the expanded version is ab + ac, i.e., multiply the term outside the bracket by everything inside the bracket (e.g.

How to factorise equations

2x(x + 3) = 2x² + 6x [remember x × x is x²]).

For an expression of the form (a + b)(c + d), the expanded version is ac + ad + bc + bd, in other words everything in the first bracket should be multiplied by everything in the second.

Example

Expand (2x + 3)(x - 1):

(2x + 3)(x - 1)

= 2x² - 2x + 3x - 3

= 2x² + x - 3

Factorising

Factorising is the reverse of expanding brackets, so it is, for example, putting 2x² + x - 3 into the form (2x + 3)(x - 1).

This is an important way of solving quadratic equations.

The first step of factorising an expression is to 'take out' any common factors which the terms have. So if you were asked to factorise x² + x, since x goes into both terms, you would write x(x + 1) .

Fact