Algebra Examples

$2 \sqrt{18 x^{3}} - 3 \sqrt{8 x^{3}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $18 x^{3}$ as ${(3 x)}^{2} \cdot (2 x)$ .

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Step 1.1.1

Factor $9$ out of $18$ .

$2 \sqrt{9 (2) x^{3}} - 3 \sqrt{8 x^{3}}$

Step 1.1.2

Rewrite $9$ as $3^{2}$ .

$2 \sqrt{3^{2} \cdot 2 x^{3}} - 3 \sqrt{8 x^{3}}$

Step 1.1.3

Factor out $x^{2}$ .

$2 \sqrt{3^{2} \cdot 2 (x^{2} x)} - 3 \sqrt{8 x^{3}}$

Step 1.1.4

Move $2$ .

$2 \sqrt{3^{2} x^{2} \cdot 2 x} - 3 \sqrt{8 x^{3}}$

Step 1.1.5

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

$2 \sqrt{{(3 x)}^{2} \cdot 2 x} - 3 \sqrt{8 x^{3}}$

Step 1.1.6

Add parentheses.

$2 \sqrt{{(3 x)}^{2} \cdot (2 x)} - 3 \sqrt{8 x^{3}}$

Step 1.2

Pull terms out from under the radical.

$2 (3 x \sqrt{2 x}) - 3 \sqrt{8 x^{3}}$

Step 1.3

Multiply $3$ by $2$ .

$6 (x \sqrt{2 x}) - 3 \sqrt{8 x^{3}}$

Step 1.4

Rewrite $8 x^{3}$ as ${(2 x)}^{2} \cdot (2 x)$ .

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Step 1.4.1

Factor $4$ out of $8$ .

$6 x \sqrt{2 x} - 3 \sqrt{4 (2) x^{3}}$

Step 1.4.2

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

$6 x \sqrt{2 x} - 3 \sqrt{2^{2} \cdot 2 x^{3}}$

Step 1.4.3

Factor out $x^{2}$ .

$6 x \sqrt{2 x} - 3 \sqrt{2^{2} \cdot 2 (x^{2} x)}$

Step 1.4.4

Move $2$ .

$6 x \sqrt{2 x} - 3 \sqrt{2^{2} x^{2} \cdot 2 x}$

Step 1.4.5

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

$6 x \sqrt{2 x} - 3 \sqrt{{(2 x)}^{2} \cdot 2 x}$

Step 1.4.6

Add parentheses.

$6 x \sqrt{2 x} - 3 \sqrt{{(2 x)}^{2} \cdot (2 x)}$

Step 1.5

Pull terms out from under the radical.

$6 x \sqrt{2 x} - 3 (2 x \sqrt{2 x})$

Step 1.6

Multiply $2$ by $- 3$ .

$6 x \sqrt{2 x} - 6 x \sqrt{2 x}$

Step 2

Subtract $6 x \sqrt{2 x}$ from $6 x \sqrt{2 x}$ .

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