A structural stability index SSS of a micro-beam is modeled as a function of its lateral displacement vvv by the expression S(v)=(2−14v)6S(v) = \left(2 - \frac{1}{4}v\right)^6S(v)=(2−41v)6. Find the first four terms of the binomial expansion of S(v)S(v)S(v) in ascending powers of vvv.
In a symmetric calibration test, the total response is defined as R(v)=(2−14v)6+(2+14v)6R(v) = \left(2 - \frac{1}{4}v\right)^6 + \left(2 + \frac{1}{4}v\right)^6R(v)=(2−41v)6+(2+41v)6. Given that vvv is sufficiently small such that terms in v4v^4v4 and higher powers of vvv may be neglected, show that R(v)=A+Bv2R(v) = A + Bv^2R(v)=A+Bv2 where AAA and BBB are integers to be determined.
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.