The amplitude of a signal in a circuit, S(t)S(t)S(t), can be modeled by the function
S(t)=(2−t4)8S(t) = \left(2 - \frac{t}{4}\right)^8S(t)=(2−4t)8
where t t\,t represents time in milliseconds.
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.
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)2F(t) = \left(3 + \frac{2}{t}\right)^2F(t)=(3+t2)2
determine the constant term in the series expansion of P(t)P(t)P(t).
Practise Edexcel A Level Maths 4.2 Expanding (a + bx)^n with exam-style questions for A Level Maths. 99 questions, 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.