Let D(v)D(v)D(v) be a function representing the density of a gas relative to its volume vvv, defined by
D(v)=(2−v8)10D(v) = \left(2 - \frac{v}{8}\right)^{10}D(v)=(2−8v)10
Find the first 4 terms of the binomial expansion of D(v)D(v)D(v) in ascending powers of vvv, giving each coefficient as an integer.
A related physical quantity Q Q\,Q is derived from the density function such that
Q=(3+2v)2D(v)Q = \left(3 + \frac{2}{v}\right)^2 D(v)Q=(3+v2)2D(v)
Hence, find the constant term in the series expansion of QQQ.
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.