Algebra Examples

$- 6 \sqrt{112 x^{3}} - 8 x \sqrt{175 x}$

Step 1

Rewrite $112 x^{3}$ as ${(4 x)}^{2} \cdot (7 x)$ .

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Step 1.1

Factor $16$ out of $112$ .

$- 6 \sqrt{16 (7) x^{3}} - 8 x \sqrt{175 x}$

Step 1.2

Rewrite $16$ as $4^{2}$ .

$- 6 \sqrt{4^{2} \cdot 7 x^{3}} - 8 x \sqrt{175 x}$

Step 1.3

Factor out $x^{2}$ .

$- 6 \sqrt{4^{2} \cdot 7 (x^{2} x)} - 8 x \sqrt{175 x}$

Step 1.4

Move $7$ .

$- 6 \sqrt{4^{2} x^{2} \cdot 7 x} - 8 x \sqrt{175 x}$

Step 1.5

Rewrite $4^{2} x^{2}$ as ${(4 x)}^{2}$ .

$- 6 \sqrt{{(4 x)}^{2} \cdot 7 x} - 8 x \sqrt{175 x}$

Step 1.6

Add parentheses.

$- 6 \sqrt{{(4 x)}^{2} \cdot (7 x)} - 8 x \sqrt{175 x}$

Step 2

Pull terms out from under the radical.

$- 6 (| 4 x | \sqrt{7 x}) - 8 x \sqrt{175 x}$

Step 3

Remove non-negative terms from the absolute value.

$- 6 (4 | x | \sqrt{7 x}) - 8 x \sqrt{175 x}$

Step 4

Multiply $4$ by $- 6$ .

$- 24 (| x | \sqrt{7 x}) - 8 x \sqrt{175 x}$

Step 5

Rewrite $175 x$ as $5^{2} \cdot (7 x)$ .

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Step 5.1

Factor $25$ out of $175$ .

$- 24 | x | \sqrt{7 x} - 8 x \sqrt{25 (7) x}$

Step 5.2

Rewrite $25$ as $5^{2}$ .

$- 24 | x | \sqrt{7 x} - 8 x \sqrt{5^{2} \cdot 7 x}$

Step 5.3

Add parentheses.

$- 24 | x | \sqrt{7 x} - 8 x \sqrt{5^{2} \cdot (7 x)}$

Step 6

Pull terms out from under the radical.

$- 24 | x | \sqrt{7 x} - 8 x (| 5 | \sqrt{7 x})$

Step 7

The absolute value is the distance between a number and zero. The distance between $0$ and $5$ is $5$ .

$- 24 | x | \sqrt{7 x} - 8 x (5 \sqrt{7 x})$

Step 8

Multiply $5$ by $- 8$ .

$- 24 | x | \sqrt{7 x} - 40 x \sqrt{7 x}$