Algebra · Lesson 7 of 16

Expanding Single Brackets

To expand a bracket, multiply each term inside by the term outside. The result has no brackets.

Secondary
Updated 14 November 2026

What you will learn

Multiply every term in a bracket by the term outside.
Handle negative signs.
Expand and simplify.

Before you start: you should be able to multiply negative numbers and collect like terms. See Collecting Like Terms.

The idea

A bracket groups terms together. The number or letter outside tells you to multiply the whole group. To expand a bracket, multiply each term inside by the term outside.

3 x (4 + 2) can be found as 3 x 4 plus 3 x 2. A rectangle split in two shows the same idea, 12 + 6 = 18.

Why it works

$3(x + 4)$ means $3$ lots of $(x + 4)$ , which is $x + 4 + x + 4 + x + 4 = 3x + 12$ . Each term inside is multiplied by $3$ .

Expanding 3(x + 4). Multiply each term inside the bracket by 3.

Negative numbers outside

A negative outside the bracket changes the sign of every term inside. $-2(x - 3) = -2x + 6$ .

Expand then simplify

After expanding you may be able to collect like terms: $2(x + 3) + 4(x - 1) = 2x + 6 + 4x - 4 = 6x + 2$ .

Worked examples

Example 1: Positive number

Expand $4(x + 3)$ .

$4 \times x = 4x$ .
$4 \times 3 = 12$ .

Answer: $4x + 12$

Example 2: Negative number

Expand $-2(x - 3)$ .

$-2 \times x = -2x$ .
$-2 \times (-3) = +6$ .

Answer: $-2x + 6$

Example 3: Simplifying

Expand and simplify $3(x + 2) + 2(x - 1)$ .

$3x + 6 + 2x - 2$ .
$5x + 4$ .

Answer: $5x + 4$

Tip: check by substituting a number such as $x = 2$ into both forms. They must give the same value.

Why it matters

Expanding brackets is used in formulas, geometry and later in quadratics. It is the reverse of factorising.

Practice

Your turn. Type or choose an answer, then press Check. Getting one wrong is fine, that is what practice is for. You can try as many times as you like.