## Expanding Brackets Removing brackets from an expression is known as expanding the expression.

This usually occurs when a term outside a bracket is multiplied by each of the terms inside the bracket.

The outside term "distributes" itself over the inside terms. Thus the name the distributive property.

### Distributive Property

When an expression is expanded, each term inside the bracket is multiplied by the term outside the bracket.

Example 1

3(x + 4) means       3 multiplied by (x + 4)          i.e. = 3 . x + 3 . 4 = 3p + 12

When brackets have been expanded, the expression must be simplified further if possible.

Example 2

5(y + 7) + 4(y + 2)
= 5y + 35 + 4y + 8
9y + 43

 Further examples Answers Expand and simplify: (a) 2(x + 7) 2(x + 7) = 2x + 14 (b) 5(3x − 6) 5(3x − 6) = 15x − 30 (c) −2(4 − 3x) −2(4 − 3x) = −8 + 6x (d) 4a(a − 3) 4a(a − 3) = 4a 2 − 12a (e) 3(x + 7) + 4(x − 2) 3(x + 7) + 4(x − 2) = 3x + 21 + 4x − 8 = 7x + 13 (f) 4x − 3(2x + 3 + 4y) 4x − 3(2x + 3 + 4y) = 4x − 6x − 9 − 12y = −2x − 12y − 9

Note When expanding a bracket with a NEGATIVE number in front, the signs of every term inside the bracket change.