Simplify the Radical Expression -10x square root of 40-2 square root of 10x^2

$- 10 x \sqrt{40} - 2 \sqrt{10 x^{2}}$

Rewrite $40$ as $2^{2} \cdot 10$ .

Factor $4$ out of $40$ .

$- 10 x \sqrt{4 (10)} - 2 \sqrt{10 x^{2}}$

Rewrite $4$ as $2^{2}$ .

$- 10 x \sqrt{2^{2} \cdot 10} - 2 \sqrt{10 x^{2}}$

Pull terms out from under the radical.

$- 10 x (| 2 | \sqrt{10}) - 2 \sqrt{10 x^{2}}$

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$- 10 x (2 \sqrt{10}) - 2 \sqrt{10 x^{2}}$

Multiply $2$ by $- 10$ .

$- 20 x \sqrt{10} - 2 \sqrt{10 x^{2}}$

Reorder $10$ and $x^{2}$ .

$- 20 x \sqrt{10} - 2 \sqrt{x^{2} \cdot 10}$

Pull terms out from under the radical.

$- 20 x \sqrt{10} - 2 | x | \sqrt{10}$