$d$) $9a + 6 \sqrt{a} + 1$
$= (3\sqrt{a})^2 + 2.3. \sqrt{a} + 1^2$
$= (3 \sqrt{a} + 1)^2$
$e$) $a^2 - 3$
$= a^2 - (\sqrt{3})^2$
$= (a-\sqrt{3})(a+\sqrt{3})$
$f$) $a^2 - 2$
$= a^2 - (\sqrt{2})^2$
$= (a - \sqrt{2})(a + \sqrt{2})$
$g$) $a-9$ ($a > 0$)
$= (\sqrt{a})^2 - 3^2$
$= (\sqrt{a} -3)(\sqrt{a}+3)$
$h$) $a-5$ ($a > 0$)
$= (\sqrt{a})^2 - (\sqrt{5})^2$
$= (\sqrt{a} -\sqrt{5})(\sqrt{a}+\sqrt{5})$
Bài $4$.
`A = {x+4.\sqrt{x} + 4}/{\sqrt{x} + 2}`
`A = {(\sqrt{x})^2 + 2.\sqrt{x}.2 + 2^2}/{\sqrt{x}+2}`
`A = {(\sqrt{x} + 2)^2}/{\sqrt{x}+2}`
`A = \sqrt{x} + 2`
`B = {x-4}/{\sqrt{x}-2}`
`B = {(\sqrt{x})^2 - 2^2}/{\sqrt{x}-2}`
`B = {(\sqrt{x} - 2)(\sqrt{x} +2)}/{\sqrt{x} -2}`
`B = \sqrt{x} + 2`
`C = {9x - 6\sqrt{x} + 1}/{3 \sqrt{x} - 1}`
`C = {(\sqrt{3x})^2 - 2.3\sqrt{x} + 1^2}/{3\sqrt{x}-1}`
`C = {(3\sqrt{x}-1})^2}/{3\sqrt{x}-1}`
`C = 3\sqrt{x}-1`
`D = {\sqrt{x^3}+1}/{x - \sqrt{x} + 1}`
`D = {\sqrt{x}.x - x + \sqrt{x} + x - \sqrt{x} + 1}/{x-\sqrt{x}+1}`
`D = {\sqrt{x}.(x - \sqrt{x} +1) + (x - \sqrt{x} + 1)}/{x-\sqrt{x}+1}`
`D = {(\sqrt{x}+1).(x - \sqrt{x} +1)}/{x-\sqrt{x}+1}`
`D = \sqrt{x}+1`
`E = {x+\sqrt{x}}/{\sqrt{x}+1}`
`E = {\sqrt{x}.(\sqrt{x}+1)}/{\sqrt{x}+1}`
`E = \sqrt{x}`.
