Expanding Single Brackets

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Preview AQA GCSE style questions on Expanding single brackets. Click "Show Solution" to see the step-by-step answer.

EasyQuestion 1

[2 marks]

Expand: (a) 4(x + 3) (b) 5(2y - 1)

MediumQuestion 2

[3 marks]

Expand and simplify: (a) 3(2x + 5) + 2(x - 4) (b) 5(y + 3) - 2(y - 1)

HardQuestion 3

[4 marks]

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

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About Expanding single brackets in AQA GCSE

Expanding brackets (also called multiplying out brackets) is a fundamental algebraic skill. It means removing the brackets by multiplying each term inside the bracket by the term outside. **The Rule:** Multiply the term outside the bracket by EVERY term inside the bracket. **Examples:** **With numbers:** 3(x + 4) = 3×x + 3×4 = 3x + 12 **With negative outside:** -2(x - 5) = -2×x + (-2)×(-5) = -2x + 10 **With variable outside:** x(x + 3) = x×x + x×3 = x² + 3x **With negative inside:** 4(2x - 3) = 4×2x + 4×(-3) = 8x - 12 **Common Mistakes to Avoid:** - Forgetting to multiply ALL terms inside the bracket - Sign errors with negative numbers - Not simplifying the final answer **Collecting Like Terms After Expanding:** When you have multiple brackets, expand each one then collect like terms. Example: 3(x + 2) + 2(x - 1) = 3x + 6 + 2x - 2 = 5x + 4 **Exam Tips:** - Write out each multiplication step to avoid errors - Be especially careful with negative signs - After expanding, always check if you can simplify