The power output PPP, in kilowatts, of a prototype wind turbine is modeled by the function $P(v) = \left(2 + \frac{v}{10}\right)^{12}$ where v≥0v \ge 0v≥0 is the wind speed in m/s. Find, in ascending powers of vvv, up to and including the term in v3v^3v3, the binomial expansion of P(v)P(v)P(v), fully simplifying each coefficient.
Use the answer to part (a) to find an approximation for the power output when the wind speed is 0.50.50.5 m/s, which corresponds to evaluating 2.05122.05^{12}2.0512. Give your answer to 2 decimal places.
Without calculating the exact value of 2.05122.05^{12}2.0512, state, with a reason, whether the answer to part (b) is an overestimate or an underestimate.
Practise Edexcel A Level Maths Binomial Expansion with exam-style questions for A Level Maths. 100 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.