Brackets in Algebra

## Brackets in Algebra

Brackets are used to control the priority of calculations, just as they do in arithmetic.

An expression such as 4(x + 3) means that the 4 multiplies both the x and the 3. Brackets are a bit like paper bags: there is x + 3 in each bag, and if there are 4 bags then there are 4 lots of x and 4 lots of 3.

Removing the brackets is called expanding the expression, or expanding the brackets. Each term in the brackets has to be multiplied by the term outside the bracket

4(x + 3)

= 4 xx x + 4 xx 3

= 4x+ 12

## Example 1

Expand 3(2x - 7)

3(2x - 7)

= 3 xx 2x - 3 xx 7 = 6x - 21

Answer: 6x - 21

## Example 2

Expand 3a(2a + 4) + 6a

Expand the brackets:

3a xx 2a + 3a xx 4 + 6a

= 6a^2 + 12a + 6a

= 6a^2 + 18a

Answer: 6a^2 + 18a