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<4B(r) = (10r + 3)\left(1 - \frac{1}{4}r\right)^{12}, \quad 0 \le r < 4B(r)=(10r+3)(1−41r)12,0≤r<4
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}(1−41r)12 giving each term in simplest form.
Hence determine the coefficient of r3r^3r3 in the expansion of B(r)B(r)B(r), giving the answer in simplest form.
Practise Edexcel A Level Maths 4.1 Expanding (1 + x)^n with exam-style questions for A Level Maths. 12 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.