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<4 B(r) = (10r + 3)\left(1 - \frac{1}{4}r\right)^{12}, \quad 0 \le r < 4 B(r)=(10r+3)(1−41r)12,0≤r<4Find 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)12giving 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.
