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Factorising is the reverse of expanding brackets and is essential for solving quadratics, simplifying expressions, and working with algebraic fractions. Students progress from single-bracket factorisation to double brackets and the difference of two squares.
Students make these errors again and again. Knowing them in advance gives you a head start.
Not taking out the highest common factor (e.g., writing 2(2x + 4) instead of 4(x + 2))
Getting signs wrong inside the brackets when factorising quadratics
Forgetting to check by expanding the brackets back out
Insights pulled from Cambridge IGCSE (0580) examiner reports — the exact mistakes candidates make every year.
You can ONLY cancel FACTORS (things multiplied), not terms added/subtracted. Factorise numerator and denominator first, then cancel matching brackets. Never cancel x² from x² − 25.
“Candidates who recognised that the numerator and denominator should be first factorised to create products were frequently successful. However, a common wrong approach was to merely cancel the x² in the first step with (x² − 25)/(x² − x − 20) = −25/(−x − 20) = 5/(x + 4), or similar, commonly seen.”
Source: CIE 0580 · November 2021 · Paper 4 · Q7a
In 'show that k = 8' questions, you must DERIVE 8, not assume it. Starting from 'k = 8' and working both ways is circular and scores zero. Work from the given info towards the target.
“This 'show that' question was often not attempted. Candidates who did attempt it often did not gain credit as they generally used the answer of k = 8 as part of their working. Candidates should be reminded that in any 'show that' question candidates must not use what they are asked to show as part of their answer.”
Source: CIE 0580 · November 2021 · Paper 3 · Q5
When raising a power to a power, MULTIPLY the exponents: (x³)³ = x⁹, not x⁶. But for coefficients like (4x³)³, the coefficient is raised: 4³ = 64, not 4 × 3 = 12.
“A small number incorrectly simplified the power by adding to give 6 rather than multiplying to give 9. Others correctly multiplied the powers but also multiplied the coefficient giving the incorrect answer of 12x⁹.”
Source: CIE 0580 · June 2024 · Paper 2 · Q21b
Based on 3of 510+ insights extracted from CIE 0580 examiner reports (2018–2024).
This topic is tested by the following exam boards. Our AI tutor covers each one with board-specific content.
Expanding brackets (distribution) is a fundamental algebraic skill used across many topics. Students multiply each term inside the bracket by the term outside, progressing to double-bracket expansion and expressions raised to powers.
Quadratic equations appear throughout the higher tier GCSE paper and are a significant step up from linear equations. Students need to factorise, complete the square, and use the quadratic formula to find solutions.
Algebraic fractions combine fraction skills with algebraic manipulation and are tested at higher tier. Students must simplify, add, subtract, multiply and divide fractions that contain variables, often needing to factorise first.
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