decompose (x^2 - 9)

I don't think decompose it the word you want.

CPhill has factorised your expression.  

that is, the factors of $${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{9}}$$ are  $${\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{3}}$$ and $${\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}$$   so

$$x^2-9=(x-3)(x+3)$$

$$x^2-9$$ is the difference (take away) of two squares   x squared and 3 squared   

$${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{9}} = {{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{{\mathtt{3}}}^{{\mathtt{2}}}$$ but it is quite the simplest form

x^2 - 9  =

(x + 3) (x - 3)