Knowledge Organiser: Quadratic Expressions
Part of Quadratic Expressions · GCSE GCSE Mathematics revision
This topic summary covers Knowledge Organiser: Quadratic Expressions within Quadratic Expressions for GCSE Mathematics. Revise Quadratic Expressions in Algebra for GCSE Mathematics with 12 exam-style questions and 22 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 8 of 8 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 8 of 8
Practice
12 questions
Recall
22 flashcards
Knowledge Organiser: Quadratic Expressions
Key Terms
- Quadratic expression: An expression with highest power x² (e.g. x² + 5x + 6)
- Expand: Multiply out brackets to remove them
- Factorise: Write as a product of two brackets
- Coefficient: The number in front of a term (e.g. the 3 in 3x²)
- Constant term: The number with no variable (the c in ax² + bx + c)
- Monic quadratic: When the coefficient of x² is 1
Must-Know Facts
- (x + a)(x + b) = x² + (a+b)x + ab
- For x² + bx + c: find two numbers that multiply to c AND add to b
- (x + 3)² = x² + 6x + 9 (NOT x² + 9)
- Difference of two squares: x² − 9 = (x+3)(x−3)
- Always check factorisation by expanding back
- If no integer pair works, the quadratic may not factorise over integers
Key Formulas
- (x + a)(x + b) = x² + (a+b)x + ab
- (a + b)² = a² + 2ab + b²
- (a − b)² = a² − 2ab + b²
- (a + b)(a − b) = a² − b²
- For ax² + bx + c (a≠1): find two numbers multiplying to ac and adding to b
Common Mistakes
- Missing middle term in (a+b)²: (x+3)² = x² + 6x + 9, not x² + 9
- ac not c: For 2x² + 7x + 3, find numbers multiplying to 2×3=6 (not just 3) and adding to 7
- Sign of constant: In (x+a)(x+b), the constant is ab — both signs affect it: (x−2)(x−3) gives +6
- Difference of two squares only works with subtraction: x² + 9 cannot be factorised (sum of two squares)
- Not simplifying: Always check if brackets can be further simplified after factorising
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Practice Questions for Quadratic Expressions
Expand (x + 5)².
Explain how to recognise whether x² + 12x + 36 is a perfect square trinomial, and write it in factorised form.
Quick Recall Flashcards
12 questions on Quadratic Expressions — practise free
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