WMA12/01 Jun 2022, Question 1: The Binomial Expansion
Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 4 marks
The question, in short
Expand (2 + (3/8)x) to the power 10, writing the first four terms in increasing powers of x, with every coefficient given as a whole number.
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Solution · 4 marks
- 1Constant term: 2¹⁰ = 1024
- 2x term: ¹⁰C₁ × 2⁹ × (3/8)x = 10 × 512 × 3/8 x = 1920x
- 3x² term: ¹⁰C₂ × 2⁸ × (3/8 x)² = 45 × 256 × 9/64 x² = 1620x²
- 4x³ term: ¹⁰C₃ × 2⁷ × (3/8 x)³ = 120 × 128 × 27/512 x³ = 810x³
- 5(2 + 3/8 x)¹⁰ = 1024 + 1920x + 1620x² + 810x³ + …
Answer1024 + 1920x + 1620x² + 810x³
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