#### Answer

$5x\sqrt{2x}$

#### Work Step by Step

$7\sqrt{32x^3}-3x\sqrt{50x}$
Factor out perfect squares.
$5\sqrt{(16)(2)(x^2)(x)}-3x\sqrt{(25)(2)(x)}$
Simplify.
$(5)(4)(x)\sqrt{2x}-(3x)(5)\sqrt{2x}$
$20x\sqrt{2x}-15x\sqrt{2x}$
Subtract like radicals.
$5x\sqrt{2x}$