Factorising
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.
What You'll Learn
- Factorising by taking out a common factor
- Factorising quadratic expressions into two brackets
- Recognising and factorising the difference of two squares
- Factorising quadratics where the coefficient of x squared is greater than 1
Watch Out For These Mistakes
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
What Examiners Say About Factorising
Insights pulled from Cambridge IGCSE (0580) examiner reports — the exact mistakes candidates make every year.
- Misconception●●●●●
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
- Presentation●●●●●
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
- Common Mistake●●●●●
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).
Exam Coverage
This topic appears in the Cambridge IGCSE past papers. Our AI tutor can help with it on any question.
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Related Topics
Expanding Brackets
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
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
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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