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Binomial Expansion

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Question 98

The first three terms, in ascending powers of xxx, of the binomial expansion of (16+5x)12(16 + 5x)^{\frac{1}{2}}(16+5x)21​ are given by

(16+5x)12≈a+58x−25512x2 (16 + 5x)^{\frac{1}{2}} \approx a + \frac{5}{8}x - \frac{25}{512}x^2 (16+5x)21​≈a+85​x−51225​x2

where aaa is a constant.

a.

State the range of values of xxx for which this expansion is valid.

Choose from the options below:

∣x∣<516∣x∣<165∣x∣<4∣x∣<1 |x| < \frac{5}{16} \quad |x| < \frac{16}{5} \quad |x| < 4 \quad |x| < 1 ∣x∣<165​∣x∣<516​∣x∣<4∣x∣<1
[2]
b.

Find the value of aaa.

Choose from the options below:

14816 1 \quad 4 \quad 8 \quad 16 14816
[2]

Binomial Expansion Questions

  1. A Level
  2. /Maths
  3. /Binomial Expansion

Practise Edexcel A Level Maths Binomial Expansion with exam-style questions for A Level Maths. 115 questions covering 4.1 Expanding (1 + x)^n, 4.2 Expanding (a + bx)^n, and 4.3 Using Partial Fractions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

Question bank