Answer
$(6\sqrt {y}-12x-25x)x\sqrt { 3xy}$.
Work Step by Step
The given expression is
$=6x\sqrt {3xy^2}-4x^2\sqrt {27xy}-5\sqrt {75x^5y}$
Factor the radicands into square terms.
$=6x\sqrt {3xy^2}-4x^2\sqrt {3^2\cdot 3xy}-5\sqrt {5^2 \cdot 3 x^4xy}$
Simplify.
$=6x\cdot \sqrt {3xy}\cdot \sqrt {y}-4x^2\cdot 3\sqrt { 3xy}-5\cdot 5x^2\sqrt { 3 xy}$
$=6\sqrt {y}\cdot x\sqrt { 3xy}-12x^2\sqrt {3xy}-25x^2\sqrt {3 xy}$.
By using the distributive property.
$=(6\sqrt {y}-12x-25x)x\sqrt { 3xy}$.
