Ta có :

a.  $xy-y\sqrt{x}+\sqrt{x}-1$

=  $y\sqrt{x}(\sqrt{x}-1)+(\sqrt{x}-1)$

=  $(\sqrt{x}-1)(y\sqrt{x}+1)$

Vậy $xy-y\sqrt{x}+\sqrt{x}-1=(\sqrt{x}-1)(y\sqrt{x}+1)$

b.  $\sqrt{ax}-\sqrt{by}+\sqrt{bx}-\sqrt{ay}$

=  $(\sqrt{ax}+\sqrt{bx})-(\sqrt{ay}+\sqrt{by})$

=  $\sqrt{x}(\sqrt{a}+\sqrt{b})-\sqrt{y}(\sqrt{a}+\sqrt{b})$

=  $(\sqrt{a}+\sqrt{b})(\sqrt{x}-\sqrt{y})$

Vậy $\sqrt{ax}-\sqrt{by}+\sqrt{bx}-\sqrt{ay}=(\sqrt{a}+\sqrt{b})(\sqrt{x}-\sqrt{y})$

c.  $\sqrt{a+b}+\sqrt{a^{2}-b^{2}}$

=  $\sqrt{a+b}+\sqrt{(a+b)(a-b)}$

=  $\sqrt{a+b}(1+\sqrt{a-b})$

Vậy $\sqrt{a+b}+\sqrt{a^{2}-b^{2}}=\sqrt{a+b}(1+\sqrt{a-b})$

d.   $12-\sqrt{x}-x=12-4\sqrt{x}+3\sqrt{x}-x$

=  $4(3-\sqrt{x})+\sqrt{x}(3-\sqrt{x})$

=  $(3-\sqrt{x})(4+\sqrt{x})$

Vậy  $12-\sqrt{x}-x=(3-\sqrt{x})(4+\sqrt{x})$