AQA · Mathematics · 8300

GCSE Maths: Factorisation: brackets

Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Factorisation: brackets (Corbettmaths Video 120), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.

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  1. What is the first step when factorising expressions like (x + 1)² + 3(x + 1)?

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    Identify the common factor. In this case, (x + 1) is the common factor that appears in both terms.

  2. After factorising out (x + 1) from (x + 1)² + 3(x + 1), what expression remains inside the new brackets?

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    (x + 1) + 3, which simplifies to (x + 4). The full factorisation is (x + 1)(x + 4).

  3. When asked to 'factorise fully' expressions like (x + 2)⁴ + (x + 2)³, what does 'fully' mean?

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    Extract all common factors, including both the bracketed term and any numerical coefficients that are common to all terms.

  4. To factorise (x + 2)⁴ + (x + 2)³ fully, the common factor is ?.

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    (x + 2)³

  5. When factorising 10(x + 1)³ + 5(x + 1)², what is the numerical part of the common factor?

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    5, which is the highest common factor of 10 and 5.

  6. In a 'hence' question like 'Hence factorise (y + 1)² + 5(y + 1) + 6', what strategy should you use?

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    Use the result from the previous part by substituting the bracketed expression for x. If x² + 5x + 6 = (x + 2)(x + 3), then replace x with (y + 1).

  7. If x² + 5x + 6 = (x + 2)(x + 3), what is the factorisation of (y + 1)² + 5(y + 1) + 6?

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    ((y + 1) + 2)((y + 1) + 3), which simplifies to (y + 3)(y + 4).

  8. When factorising (x + 8)⁷ + (x + 8)⁶(3x − 1), what power of (x + 8) is the common factor?

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    (x + 8)⁶, which is the lowest power present in both terms.

  9. After factorising out (x + 8)⁶ from (x + 8)⁷ + (x + 8)⁶(3x − 1), what remains in the brackets?

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    (x + 8) + (3x − 1), which simplifies to 4x + 7. The full factorisation is (x + 8)⁶(4x + 7).

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