The sensitivity of a signal processor, S(x)S(x)S(x), is modeled by the function S(x)=(2x−1.5)10S(x) = (2x - 1.5)^{10}S(x)=(2x−1.5)10 Show that the first three terms, in descending powers of xxx, of the expansion of S(x)S(x)S(x) are given by 1024x10+ax9+bx81024x^{10} + ax^9 + bx^81024x10+ax9+bx8 where aaa and bbb are integers to be found.
In a modified design, the processor response is governed by the expansion of (2x−32x)10\left(2x - \frac{3}{2x}\right)^{10}(2x−2x3)10 Find the constant term in this expansion.