Brackets in Algebra

Brackets in Algebra

GCSE(F), GCSE(H),

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 needs to multiply 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. Each term in the brackets has to be multiplied by the term outside the bracket. The terms in the brackets can be treated as a list and multiplying each item in the list by the factor outside the bracket: for example, expand 4(x + 3):

4 x x = 4x

4 x 3 = 12

so that 4(x+ 3) = 4x+ 12.

Examples

1. Expand 3(2x - 7)

Answer: 6x - 21

3 x 2x = 6x 3 x 7 = 21

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

Answer: 6a2 + 18a

Expand the brackets:

3a x 2a = 6a2

3a x 4 = 12a

Add in the 6a from the end: 6a2 + 12a + 6a

= 6a2 + 18a