Simplify x square root of 2x^3-4x^2 square root of 128x

$x \sqrt{2 x^{3}} - 4 x^{2} \sqrt{128 x}$

Simplify each term.

Rewrite $2 x^{3}$ as $x^{2} \cdot (2 x)$ .

Factor out $x^{2}$ .

$x \sqrt{2 (x^{2} x)} - 4 x^{2} \sqrt{128 x}$

Reorder $2$ and $x^{2}$ .

$x \sqrt{x^{2} \cdot 2 x} - 4 x^{2} \sqrt{128 x}$

Add parentheses.

$x \sqrt{x^{2} \cdot (2 x)} - 4 x^{2} \sqrt{128 x}$

Pull terms out from under the radical.

$x (x \sqrt{2 x}) - 4 x^{2} \sqrt{128 x}$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$x \cdot x \sqrt{2 x} - 4 x^{2} \sqrt{128 x}$

Multiply $x$ by $x$ .

$x^{2} \sqrt{2 x} - 4 x^{2} \sqrt{128 x}$

Rewrite $128 x$ as $8^{2} \cdot (2 x)$ .

Factor $64$ out of $128$ .

$x^{2} \sqrt{2 x} - 4 x^{2} \sqrt{64 (2) x}$

Rewrite $64$ as $8^{2}$ .

$x^{2} \sqrt{2 x} - 4 x^{2} \sqrt{8^{2} \cdot 2 x}$

Add parentheses.

$x^{2} \sqrt{2 x} - 4 x^{2} \sqrt{8^{2} \cdot (2 x)}$

Pull terms out from under the radical.

$x^{2} \sqrt{2 x} - 4 x^{2} (8 \sqrt{2 x})$

Multiply $8$ by $- 4$ .

$x^{2} \sqrt{2 x} - 32 x^{2} \sqrt{2 x}$

Subtract $32 x^{2} \sqrt{2 x}$ from $x^{2} \sqrt{2 x}$ .

$- 31 x^{2} \sqrt{2 x}$