Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Rewrite $5 x^{3}$ as $x^{2} \cdot (5 x)$ .

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Step 1.1.1

Factor out $x^{2}$ .

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

Step 1.1.2

Reorder $5$ and $x^{2}$ .

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

Step 1.1.3

Add parentheses.

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

Step 1.2

Pull terms out from under the radical.

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

Step 1.3

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 1.3.1

Move $x$ .

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

Step 1.3.2

Multiply $x$ by $x^{2}$ .

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Step 1.3.2.1

Raise $x$ to the power of $1$ .

$- 2 x^{3} \sqrt{5 x} + 5 (x^{1} x^{2}) \sqrt{5 x}$

Step 1.3.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 2 x^{3} \sqrt{5 x} + 5 x^{1 + 2} \sqrt{5 x}$

Step 1.3.3

Add $1$ and $2$ .

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

Step 2

Add $- 2 x^{3} \sqrt{5 x}$ and $5 x^{3} \sqrt{5 x}$ .

$3 x^{3} \sqrt{5 x}$