In a materials science laboratory, the expansion factor of a synthetic polymer PPP relative to temperature change ttt is modeled by the function:
P(t)=(2+kt4)5P(t) = \left(2 + \frac{kt}{4}\right)^5P(t)=(2+4kt)5
where kkk is a non-zero constant.
Find the first 4 terms, in ascending powers of ttt, of the binomial expansion of P(t)P(t)P(t). Give each term in its simplest form.
To account for sensor drift, a corrected expansion model R(t)R(t)R(t) is defined as:
R(t)=(5+3t)P(t)R(t) = (5 + 3t)P(t)R(t)=(5+3t)P(t)
Given that in the expansion of R(t)R(t)R(t), the coefficient of the ttt term is equal to the constant term, determine the value of kkk.
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.