Expand and simplify1 markBoth boards
Expand and simplify (2x − 3)(x + 5).
Show the mark scheme and the examiner note
Answer: 2x² + 7x − 15
- Four products: 2x·x, 2x·5, −3·x, −3·5
- 2x² + 10x − 3x − 15
- Collect: 2x² + 7x − 15
- A. 2x² + 7x − 15 — Correct: 2x² + 10x − 3x − 15 collects to 2x² + 7x − 15.
- B. 2x² + 7x + 15 — The constant is wrong: (−3) × (+5) = −15, and the sign goes with it.
- C. 2x² − 7x − 15 — The x term sign is wrong: +10x and −3x make +7x.
- D. 2x² + 2x − 15 — The x terms were combined as 10 − 3 in the wrong order, giving 2x instead of 7x.
Examiner technique: Write all four products before collecting. Skipping a term is the single most common error in this question type, and it costs the whole mark rather than part of it.