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Binomial Expansion

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Question 109

The strength of a magnetic field BBB, measured in microteslas, at a distance rrr cm from a specific electronic component is modeled by the function:

B(r)=(10r+3)(1−14r)12,0≤r<4 B(r) = (10r + 3)\left(1 - \frac{1}{4}r\right)^{12}, \quad 0 \le r < 4 B(r)=(10r+3)(1−41​r)12,0≤r<4
a.

Find the first four terms, in ascending powers of rrr, of the binomial expansion of

(1−14r)12 \left(1 - \frac{1}{4}r\right)^{12} (1−41​r)12

giving each term in simplest form.

[4]
b.

Hence determine the coefficient of r3r^3r3 in the expansion of B(r)B(r)B(r), giving the answer in simplest form.

[3]

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