Algebra Examples

$2 \sqrt{2 x^{3}} + 4 x \sqrt{8 x}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor out $x^{2}$ .

$2 \sqrt{2 (x^{2} x)} + 4 x \sqrt{8 x}$

Step 1.1.2

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

$2 \sqrt{x^{2} \cdot 2 x} + 4 x \sqrt{8 x}$

Step 1.1.3

Add parentheses.

$2 \sqrt{x^{2} \cdot (2 x)} + 4 x \sqrt{8 x}$

$2 \sqrt{x^{2} \cdot (2 x)} + 4 x \sqrt{8 x}$

Step 1.2

Pull terms out from under the radical.

$2 (x \sqrt{2 x}) + 4 x \sqrt{8 x}$

Step 1.3

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

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Step 1.3.1

Factor $4$ out of $8$ .

$2 x \sqrt{2 x} + 4 x \sqrt{4 (2) x}$

Step 1.3.2

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

$2 x \sqrt{2 x} + 4 x \sqrt{2^{2} \cdot 2 x}$

Step 1.3.3

Add parentheses.

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

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

Step 1.4

Pull terms out from under the radical.

$2 x \sqrt{2 x} + 4 x (2 \sqrt{2 x})$

Step 1.5

Multiply $2$ by $4$ .

$2 x \sqrt{2 x} + 8 x \sqrt{2 x}$

$2 x \sqrt{2 x} + 8 x \sqrt{2 x}$

Step 2

Add $2 x \sqrt{2 x}$ and $8 x \sqrt{2 x}$ .

$10 x \sqrt{2 x}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$