Expanding an expression with a single bracket means multiplying every term inside the bracket by the term outside it. This uses the distributive law.

 

A number or letter written next to a bracket multiplies everything inside the bracket.

 

For example:

$$
3(x + 4)
$$

 

Multiply \( 3 \) by each term inside the bracket:

$$
3 \times x + 3 \times 4
$$

$$
= 3x + 12
$$

 

 

Expanding with subtraction inside the bracket

The same rule applies when there is a minus sign inside the bracket.

 

For example:

$$
5(x - 2)
$$

 

Multiply each term:

$$
5 \times x - 5 \times 2
$$

$$
= 5x - 10
$$

 

 

Expanding with a negative outside the bracket

If the term outside the bracket is negative, every term inside the bracket changes sign.

 

For example:

$$
-2(x + 3)
$$

$$
= -2x - 6
$$

 

Another example:

$$
-(x - 5)
$$

$$
= -x + 5
$$

 

 

Expanding brackets with numbers and variables

For example:

$$
4(2x + 7)
$$

$$
= 8x + 28
$$

 

Always check that:
• every term inside the bracket has been multiplied
• signs are handled carefully

 

Expanding single brackets correctly is an essential step before collecting like terms or solving equations.