Expanding Brackets and Factorising

Expanding brackets and factorising are two of the most important algebraic skills in AQA GCSE Mathematics. They are essentially opposite operations: expanding removes brackets from an expression, while factorising puts them in. Mastering both skills is essential for solving equations, simplifying expressions, and tackling quadratics at every grade level.

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Expanding a Single Bracket

To expand a single bracket, multiply every term inside the bracket by the term outside.

Rule

a(b + c) = ab + ac

Worked Example 1

Expand: 3(2x + 5)

Multiply each term inside the bracket by 3:

• 3 x 2x = 6x
• 3 x 5 = 15

Answer: 6x + 15

Worked Example 2

Expand: -2(4y - 3)

Multiply each term inside the bracket by -2:

• -2 x 4y = -8y
• -2 x (-3) = +6

Answer: -8y + 6

Exam Tip: Take extra care with negative signs when expanding. The most common error is forgetting that a negative multiplied by a negative gives a positive.

Worked Example 3

Expand and simplify: 3(x + 4) + 2(x - 1)