The sensitivity of a signal processor, $S(x)$, is modeled by the function

$$S(x)=(2x-1.5{)}^{10}$$

Show that the first three terms, in descending powers of $x$, of the expansion of $S(x)$ are given by

$$1024x^{10}+a{x}^9+b{x}^8$$

where $a$ and $b$ are integers to be found.

In a modified design, the processor response is governed by the expansion of

$${\left(2x-\frac{3}{2x}\right)}^{10}$$

Find the constant term in this expansion.