Algebra Examples

$- 5 x^{2} \sqrt{2 x} + x \sqrt{200 x^{3}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $200 x^{3}$ as ${(10 x)}^{2} \cdot (2 x)$ .

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Step 1.1.1

Factor $100$ out of $200$ .

$- 5 x^{2} \sqrt{2 x} + x \sqrt{100 (2) x^{3}}$

Step 1.1.2

Rewrite $100$ as $10^{2}$ .

$- 5 x^{2} \sqrt{2 x} + x \sqrt{10^{2} \cdot 2 x^{3}}$

Step 1.1.3

Factor out $x^{2}$ .

$- 5 x^{2} \sqrt{2 x} + x \sqrt{10^{2} \cdot 2 (x^{2} x)}$

Step 1.1.4

Move $2$ .

$- 5 x^{2} \sqrt{2 x} + x \sqrt{10^{2} x^{2} \cdot 2 x}$

Step 1.1.5

Rewrite $10^{2} x^{2}$ as ${(10 x)}^{2}$ .

$- 5 x^{2} \sqrt{2 x} + x \sqrt{{(10 x)}^{2} \cdot 2 x}$

Step 1.1.6

Add parentheses.

$- 5 x^{2} \sqrt{2 x} + x \sqrt{{(10 x)}^{2} \cdot (2 x)}$

Step 1.2

Pull terms out from under the radical.

$- 5 x^{2} \sqrt{2 x} + x (10 x \sqrt{2 x})$

Step 1.3

Rewrite using the commutative property of multiplication.

$- 5 x^{2} \sqrt{2 x} + 10 x (x \sqrt{2 x})$

Step 1.4

Multiply $x$ by $x$ by adding the exponents.

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Step 1.4.1

Move $x$ .

$- 5 x^{2} \sqrt{2 x} + 10 (x \cdot x) \sqrt{2 x}$

Step 1.4.2

Multiply $x$ by $x$ .

$- 5 x^{2} \sqrt{2 x} + 10 x^{2} \sqrt{2 x}$

Step 2

Add $- 5 x^{2} \sqrt{2 x}$ and $10 x^{2} \sqrt{2 x}$ .

$5 x^{2} \sqrt{2 x}$