a) x - 9 = ($\sqrt{x}$ - 3)($\sqrt{x}$ + 3)

b) x - 5$\sqrt{x}$ + 4 = x - $\sqrt{x}$ - 4$\sqrt{x}$ + 4 = $\sqrt{x}$($\sqrt{x}$ - 1) - 4($\sqrt{x}$ - 1) = ($\sqrt{x}$ - 1)($\sqrt{x}$ - 4).

c) 6$\sqrt{xy}$ - 4x$\sqrt{x}$ - 9y$\sqrt{y}$ + 6xy = 2$\sqrt{x}$(3$\sqrt{y}$ - 2x) - 3y(3$\sqrt{y}$ - 2x) = (3$\sqrt{y}$ - 2x)(2$\sqrt{x}$ - 3y) 

d) x - 2$\sqrt{x - 1}$ - $a^{2}$ = (x - 1 - 2$\sqrt{x - 1}$ + 1) - $a^{2}$

= $(\sqrt{x - 1} - 1)^{2}$ - $a^{2}$ = ($\sqrt{x - 1}$ - 1 - a)($\sqrt{x - 1}$ - 1 + a).