Exam-style question
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Which first step is most appropriate when expanding and simplifying (2x - 3)(x + 5) - x(x - 1)?.
- A.B6: choose the method that matches Manipulate polynomials algebraically
- B.Use any familiar GCSE calculation even if it ignores Manipulate polynomials algebraically
- C.Write only the final answer without showing the mathematical method
- D.Change the notation or restrictions to make the algebra look simpler
Model answer
What a good answer should say
- The correct answer is B6: choose the method that matches Manipulate polynomials algebraically.
- Expand each bracket carefully, collect like powers of x, and then simplify the polynomial term by term.
This answer is tied to the objective: B6 Manipulate polynomials algebraically, including expanding brackets and collecting like terms, factorisation and simple algebraic division; use the factor theorem; simplify rational expressions including by factorising and cancelling, and algebraic division by linear expressions only..
Explanation
Why this works
Use the explanation to connect the worked answer back to B6 Manipulate polynomials algebraically, including expanding brackets and collecting like terms, factorisation and simple algebraic division; use the factor theorem; simplify rational expressions including by factorising and cancelling, and algebraic division by linear expressions only..
The correct option, B6: choose the method that matches Manipulate polynomials algebraically, is supported because this item is about expanding brackets and collecting like terms. A valid solution keeps x^2 terms, x terms and constant terms separate before combining them.
The distractors are weaker because they skip the polynomial structure or treat unlike terms as if they can be combined.
Maths method check
- Topic focus: Pure Mathematics.
- Question style: practice.
- Reasoning demand: recall.
- Check the operation, notation, units, and final answer form against the question before moving on.
Common mistake
No common mistake is linked to this question yet.