Ta có :

a.  $ab+b\sqrt{a}+\sqrt{a}+1$

= $b\sqrt{a}(\sqrt{a}+1)+(\sqrt{a}+1)$

= $(\sqrt{a}+1)(b\sqrt{a}+1)$

Vậy $ab+b\sqrt{a}+\sqrt{a}+1$ = $(\sqrt{a}+1)(b\sqrt{a}+1)$

b.   $\sqrt{x^{3}}-\sqrt{y^{3}}+\sqrt{x^{2}y}-\sqrt{xy^{2}}$

=  $(\sqrt{x^{3}}+\sqrt{x^{2}y})-(\sqrt{y^{3}}+\sqrt{xy^{2}})$

= $\sqrt{x^{2}}(\sqrt{x}+\sqrt{y})-\sqrt{y^{2}}(\sqrt{y}+\sqrt{x})$

= $\left ( \sqrt{x}+\sqrt{y} \right )\left (  \sqrt{x^{2}}-\sqrt{y^{2}}\right )=\left ( \sqrt{x}+\sqrt{y} \right )\left ( x-y \right )$

Vậy $\sqrt{x^{3}}-\sqrt{y^{3}}+\sqrt{x^{2}y}-\sqrt{xy^{2}}$ = $\left ( \sqrt{x}+\sqrt{y} \right )\left ( x-y \right )$