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* = 4*x*

4 x 3 = 12

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

1. Expand 3(2*x* - 7)

Answer: 6*x* - 21

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

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

Answer: 6*a*^{2} + 18*a*

Expand the brackets:

3*a* x 2*a* = 6*a*^{2}

3*a* x 4 = 12*a*

Add in the 6*a* from the end: 6*a*^{2} + 12*a* + 6*a*

= 6*a*^{2} + 18*a*

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