WMA12/01 Jan 2021, Question 4: The Binomial Expansion
Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 8 marks
The question, in short
Expand (2 + px)⁶ up to the x² term with p constant, then use a given x² coefficient from multiplying by (3 − ½x) to determine p.
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Part (a) · 4 marks
Write the first three terms of the expansion of (2 + px)⁶ in increasing powers of x, simplifying each term.
- 1(2 + px)⁶ = 2⁶ + 6 × 2⁵(px) + (6 × 5)/2 × 2⁴(px)² + …
- 2= 64 + 6 × 32px + 15 × 16p²x² + …
- 3= 64 + 192px + 240p²x² + …
Answer64 + 192px + 240p²x²
Part (b) · 4 marks
Using the stated coefficient of x² in (3 − ½x)(2 + px)⁶ being −3/4, work out the values p can take.
- 1x² terms of (3 − ½x)(64 + 192px + 240p²x²): 3 × 240p² and (−½) × 192p
- 2Coefficient of x²: 720p² − 96p = −3/4
- 32880p² − 384p + 3 = 0
- 4(8p − 1)(360p − 3) = 0
- 5p = 1/8 or p = 1/120
Answerp = 1/8 or p = 1/120
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