Answer
$-10x^3y\sqrt{ 6y}$.
Work Step by Step
The given expression is
$=4x\sqrt{6x^4y^3}-7y\sqrt{24x^6y}$
Factor the radicands using perfect square factors.
$=4x\sqrt{6x^4y^2y}-7y\sqrt{2^2\cdot 2\cdot 3x^6y}$
Group the perfect square factors.
$=4x\sqrt{(x^4y^2)(6y)}-7y\sqrt{(2^2x^6)( 2\cdot 3y)}$
Factor into two radicals.
$=4x\sqrt{(x^4y^2)}\sqrt{(6y)}-7y\sqrt{(2^2x^6)}\sqrt{( 6y)}$
Simplify.
$=4x\cdot x^2y\sqrt{6y}-7y\cdot 2x^3\sqrt{ 6y}$
$=4 x^3y\sqrt{6y}-14x^3y\sqrt{ 6y}$
Use the distributive property.
$=(4 -14)x^3y\sqrt{ 6y}$
Simplify.
$=-10x^3y\sqrt{ 6y}$.
