Algebra Examples

$- 4 x \sqrt{125 x^{2}} + 5 \sqrt{125 x^{4}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $125 x^{2}$ as ${(5 x)}^{2} \cdot 5$ .

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Step 1.1.1

Factor $25$ out of $125$ .

$- 4 x \sqrt{25 (5) x^{2}} + 5 \sqrt{125 x^{4}}$

Step 1.1.2

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

$- 4 x \sqrt{5^{2} \cdot 5 x^{2}} + 5 \sqrt{125 x^{4}}$

Step 1.1.3

Move $5$ .

$- 4 x \sqrt{5^{2} x^{2} \cdot 5} + 5 \sqrt{125 x^{4}}$

Step 1.1.4

Rewrite $5^{2} x^{2}$ as ${(5 x)}^{2}$ .

$- 4 x \sqrt{{(5 x)}^{2} \cdot 5} + 5 \sqrt{125 x^{4}}$

Step 1.2

Pull terms out from under the radical.

$- 4 x (| 5 x | \sqrt{5}) + 5 \sqrt{125 x^{4}}$

Step 1.3

Remove non-negative terms from the absolute value.

$- 4 x (5 | x | \sqrt{5}) + 5 \sqrt{125 x^{4}}$

Step 1.4

Multiply $5$ by $- 4$ .

$- 20 x (| x | \sqrt{5}) + 5 \sqrt{125 x^{4}}$

Step 1.5

Rewrite $125 x^{4}$ as ${(5 x^{2})}^{2} \cdot 5$ .

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Step 1.5.1

Factor $25$ out of $125$ .

$- 20 x (| x | \sqrt{5}) + 5 \sqrt{25 (5) x^{4}}$

Step 1.5.2

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

$- 20 x (| x | \sqrt{5}) + 5 \sqrt{5^{2} \cdot 5 x^{4}}$

Step 1.5.3

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

$- 20 x (| x | \sqrt{5}) + 5 \sqrt{5^{2} \cdot 5 {(x^{2})}^{2}}$

Step 1.5.4

Move $5$ .

$- 20 x (| x | \sqrt{5}) + 5 \sqrt{5^{2} {(x^{2})}^{2} \cdot 5}$

Step 1.5.5

Rewrite $5^{2} {(x^{2})}^{2}$ as ${(5 x^{2})}^{2}$ .

$- 20 x (| x | \sqrt{5}) + 5 \sqrt{{(5 x^{2})}^{2} \cdot 5}$

Step 1.6

Pull terms out from under the radical.

$- 20 x (| x | \sqrt{5}) + 5 (| 5 x^{2} | \sqrt{5})$

Step 1.7

Remove non-negative terms from the absolute value.

$- 20 x (| x | \sqrt{5}) + 5 (5 x^{2} \sqrt{5})$

Step 1.8

Multiply $5$ by $5$ .

$- 20 x (| x | \sqrt{5}) + 25 x^{2} \sqrt{5}$

Step 2

Reorder factors in $- 20 x (| x | \sqrt{5}) + 25 x^{2} \sqrt{5}$ .

$- 20 x | x | \sqrt{5} + 25 x^{2} \sqrt{5}$