A2AlgebraFoundation

Expanding Brackets

Expanding (or “multiplying out”) brackets means getting rid of the brackets by multiplying everything inside by what is outside. It is the reverse of factorising.

35 min Video by Maths Genie AQA GCSE Maths

Expanding Single BracketsWatch the walkthrough, then read the notes below.

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What you'll learn

Expand a single bracket
Expand and simplify
Expand double brackets (FOIL)
Avoid sign mistakes

Single brackets

Multiply the term outside by each term inside: $3 (x + 2) = 3 x + 6$ . Watch the signs carefully when the outside term is negative.

4 \times 2 x = 8 x

4 \times - 3 = - 12

Answer

8 x - 12

Double brackets

Each term in the first bracket multiplies each term in the second — a method often called FOIL (First, Outer, Inner, Last). Then collect like terms.

(x + a) (x + b) = x^{2} + (a + b) x + ab

Expanding two brackets.

x \cdot x = x^{2}

; outer

4 x

; inner

3 x

; last

12

2Collect:

x^{2} + 7 x + 12

Answer

x^{2} + 7 x + 12

Tip — A negative times a negative is positive — a common place to slip up.

Remember these

a (b + c) = ab + a c

Single bracket.

(x + a) (x + b) = x^{2} + (a + b) x + ab

Double brackets.

Watch out for these

Only multiplying the first term:

3 (x + 2) = 3 x + 2

Multiply everything inside:

3 x + 6

Getting the sign wrong:

- 2 (x - 3) = - 2 x - 6

- 2 \times - 3 = + 6

, so

- 2 x + 6

Key takeaways

Multiply the outside term by every term inside.
Double brackets: multiply each pair (FOIL), then collect like terms.
Take care with negative signs.

Test yourself

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