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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.
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.
Source: CIE 0580 · May/June 2021 · Paper 3 · Q5
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.
Source: CIE 0580 · May/June 2021 · Paper 4 · Q7a
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.
Source: CIE 0580 · Feb/March 2024 · Paper 2 · Q21b
Based on 3of 500+ insights extracted from CIE 0580 examiner reports (2018–2024).
This topic appears in the Cambridge IGCSE past papers. Our AI tutor can help with it on any question.
Useful for this topic:
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 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 a step up from basic fractions. Students must simplify, add, subtract, multiply and divide fractions that contain variables, often needing to factorise first.
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