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Binomial Expansion

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Question 263

The amplitude of a signal in a circuit, S(t)S(t)S(t), can be modeled by the function

S(t)=(2−t4)8 S(t) = \left(2 - \frac{t}{4}\right)^8 S(t)=(2−4t​)8

where t t\,t represents time in milliseconds.

a.

Find the first 4 terms, in ascending powers of ttt, of the binomial expansion of S(t)S(t)S(t), giving each term in its simplest form.

[4]
b.

A noise-cancelling filter F(t)F(t)F(t) is applied such that the resulting signal is given by the product P(t)=F(t)S(t)P(t) = F(t)S(t)P(t)=F(t)S(t). Given that

F(t)=(3+2t)2 F(t) = \left(3 + \frac{2}{t}\right)^2 F(t)=(3+t2​)2

determine the constant term in the series expansion of P(t)P(t)P(t).

[3]
Markscheme

Binomial Expansion Questions

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

408 exam-style questions on Edexcel A Level Maths Binomial Expansion, covering 4.1 Expanding (1 + x)^n, 4.2 Expanding (a + bx)^n, and 4.3 Using Partial Fractions. Each one has a worked solution and a mark scheme showing where the marks go.

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