Giả sử các căn đều có nghĩa
1)
$\sqrt{x^2 - y^2}$ + $\sqrt{x - y}$
= $\sqrt{(x - y)(x + y)}$ + $\sqrt{x - y}$
= $\sqrt{x - y}$($\sqrt{x + y}$ + 1)
2)
x + y + 2$\sqrt{xy}$
`= (\sqrt{x} + \sqrt{y})^2`
3)
$\sqrt{ax}$ - $\sqrt{ay}$ + $\sqrt{bx}$ - $\sqrt{by}$
= $\sqrt{a}$($\sqrt{x}$ - $\sqrt{y}$) + $\sqrt{b}$($\sqrt{x}$ - $\sqrt{y}$)
= ($\sqrt{x}$ - $\sqrt{y}$)($\sqrt{a}$ + $\sqrt{b}$)
4)
x + y - z + 2$\sqrt{xy}$
`= (\sqrt{x} + \sqrt{y})^2 - z`
= ($\sqrt{x}$ + $\sqrt{y}$ + $\sqrt{z}$)($\sqrt{x}$ + $\sqrt{y}$ - $\sqrt{z}$)
5)
x + 5$\sqrt{x}$ - 6
= x - $\sqrt{x}$ + 6$\sqrt{x}$ - 6
= $\sqrt{x}$($\sqrt{x}$ - 1) + 6($\sqrt{x}$ - 1)
= ($\sqrt{x}$ - 1)($\sqrt{x}$ + 6)
