Simplify a square root of b+ square root of a^2b- square root of ab^3

$a \sqrt{b} + \sqrt{a^{2} b} - \sqrt{a b^{3}}$

Step 1

Simplify each term.

Pull terms out from under the radical.

$a \sqrt{b} + a \sqrt{b} - \sqrt{a b^{3}}$

Rewrite $a b^{3}$ as $b^{2} (a b)$ .

Factor out $b^{2}$ .

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

Reorder $a$ and $b^{2}$ .

$a \sqrt{b} + a \sqrt{b} - \sqrt{b^{2} a b}$

Add parentheses.

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

Pull terms out from under the radical.

$a \sqrt{b} + a \sqrt{b} - b \sqrt{a b}$

Step 2

Add $a \sqrt{b}$ and $a \sqrt{b}$ .

$2 a \sqrt{b} - b \sqrt{a b}$