Expressions, formulae and equations
Expanding brackets
The number outside the bracket multiplies everything inside it — every term, without exception.
What expanding means
To expand a bracket, multiply EACH term inside by the term outside. It is also called 'multiplying out the brackets'. 4(n + 3) means 4 × (n + 3), but you write it without the × sign. 4(n + 3) = 4 × n + 4 × 3 = 4n + 12
When there is a minus sign
2(x − 5) = 2 × x − 2 × 5 = 2x − 10 The minus sign stays: you are taking away 10 from the 2x. Multiply the 5 by the 2, then subtract.
Three terms inside
3(2g + h − 7) = 3 × 2g + 3 × h − 3 × 7 = 6g + 3h − 21 Note 3 × 2g is 3 × 2 × g, which simplifies to 6g. Every term inside gets multiplied — miss one and the whole answer is wrong.
Worked examples
Expand 4(n + 3)
- Multiply each term inside by the 4.
- 4 × n = 4n and 4 × 3 = 12.
Answer: 4n + 12
Expand 2(x − 5)
- 2 × x = 2x.
- 2 × 5 = 10, and the minus sign stays.
Answer: 2x − 10
Expand 3(2g + h − 7)
- 3 × 2g = 6g.
- 3 × h = 3h.
- 3 × 7 = 21, with the minus sign kept.
Answer: 6g + 3h − 21
Why 3 × 2g is 6g
- 3 × 2g means 3 × 2 × g.
- 3 × 2 = 6.
Answer: 6g
Expand 5(a + 2)
- 5 × a = 5a.
- 5 × 2 = 10.
Answer: 5a + 10
The commonest mistake
- Multiplying only the first term inside.
- 4(n + 3) is NOT 4n + 3.
Answer: Every term inside must be multiplied
Where you see this in real life
- Buying 4 meal deals, each a £3 sandwich and a £2 drink, costs 4(3 + 2) = 4 × 3 + 4 × 2 = £20 either way.
- Expanding is how you check two different-looking price formulas are actually the same.
Key words
- Brackets
- symbols grouping terms that are treated as one
- Expand
- multiply out a bracket
- Multiply out
- another name for expanding a bracket
- Term
- one part of an expression, separated by + or −