The structural load L(w)L(w)L(w) of a specific beam under stress is modeled by the function L(w)=(5+3w)(2+kw)4L(w) = (5 + 3w)(2 + kw)^4L(w)=(5+3w)(2+kw)4, where www represents the deflection in millimetres and kkk is a stiffness constant.
Find the first three terms, in ascending powers of www, of the binomial expansion of (2+kw)4(2 + kw)^4(2+kw)4 where kkk is a constant. Give each term in its simplest form.
Given that in the expansion of L(w)L(w)L(w) the coefficient of w2w^2w2 is 24, determine the possible values of the stiffness constant kkk.