Algebra Examples

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

Step 1

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

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Step 1.1

Factor $4$ out of $40$ .

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

Step 1.2

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

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

Step 4

Multiply $2$ by $- 10$ .

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

Step 5

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

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

Step 6

Pull terms out from under the radical.

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