Answer
$-11xy\sqrt { 2x}$.
Work Step by Step
The given expression is
$=3x\sqrt {8xy^2}-5y\sqrt {32x^3}+\sqrt {18x^3y^2}$
Factor the radicands into square terms.
$=3x\sqrt {2^2\cdot 2xy^2}-5y\sqrt {4^2\cdot2x^2\cdot x}+\sqrt {3^2\cdot 2x^2\cdot xy^2}$
Simplify.
$=3x\cdot 2 y\sqrt { 2x}-5y\cdot 4x\sqrt {2x}+3xy\sqrt {2 x}$
$=6xy\sqrt { 2x}-20xy\sqrt {2x}+3xy\sqrt {2 x}$
By using the distributive property:
$=(6-20+3)xy\sqrt { 2x}$
Simplify.
$=(-11)xy\sqrt { 2x}$
$=-11xy\sqrt { 2x}$.
