Answer
$\sqrt{a^{3}b^{5}}-2\sqrt{a^{7}b^{3}}+\sqrt{a^{3}b^{9}}=ab(b-2a^{2}+b^{3})\sqrt{ab}$
Work Step by Step
$\sqrt{a^{3}b^{5}}-2\sqrt{a^{7}b^{3}}+\sqrt{a^{3}b^{9}}$
Simplify each square root:
$\sqrt{a^{3}b^{5}}-2\sqrt{a^{7}b^{3}}+\sqrt{a^{3}b^{9}}=...$
$...=ab^{2}\sqrt{ab}-2a^{3}b\sqrt{ab}+ab^{4}\sqrt{ab}=...$
The expressions inside square roots are all the same. Simplify by adding the coefficients:
$...=(ab^{2}-2a^{3}b+ab^{4})\sqrt{ab}=...$
Take out common factor $ab$ from the expression inside parentheses:
$...=ab(b-2a^{2}+b^{3})\sqrt{ab}$
