Algebra Examples

$3 x \sqrt{25 x^{3}} - x \sqrt{4 x^{3}} + 3 x \sqrt{9 x^{3}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $25 x^{3}$ as ${(5 x)}^{2} x$ .

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Step 1.1.1

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

$3 x \sqrt{5^{2} x^{3}} - x \sqrt{4 x^{3}} + 3 x \sqrt{9 x^{3}}$

Step 1.1.2

Factor out $x^{2}$ .

$3 x \sqrt{5^{2} (x^{2} x)} - x \sqrt{4 x^{3}} + 3 x \sqrt{9 x^{3}}$

Step 1.1.3

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

$3 x \sqrt{{(5 x)}^{2} x} - x \sqrt{4 x^{3}} + 3 x \sqrt{9 x^{3}}$

Step 1.2

Pull terms out from under the radical.

$3 x (5 x \sqrt{x}) - x \sqrt{4 x^{3}} + 3 x \sqrt{9 x^{3}}$

Step 1.3

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

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Step 1.3.1

Move $x$ .

$3 (x \cdot x) (5 \sqrt{x}) - x \sqrt{4 x^{3}} + 3 x \sqrt{9 x^{3}}$

Step 1.3.2

Multiply $x$ by $x$ .

$3 x^{2} (5 \sqrt{x}) - x \sqrt{4 x^{3}} + 3 x \sqrt{9 x^{3}}$

Step 1.4

Multiply $5$ by $3$ .

$15 x^{2} \sqrt{x} - x \sqrt{4 x^{3}} + 3 x \sqrt{9 x^{3}}$

Step 1.5

Rewrite $4 x^{3}$ as ${(2 x)}^{2} x$ .

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Step 1.5.1

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

$15 x^{2} \sqrt{x} - x \sqrt{2^{2} x^{3}} + 3 x \sqrt{9 x^{3}}$

Step 1.5.2

Factor out $x^{2}$ .

$15 x^{2} \sqrt{x} - x \sqrt{2^{2} (x^{2} x)} + 3 x \sqrt{9 x^{3}}$

Step 1.5.3

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

$15 x^{2} \sqrt{x} - x \sqrt{{(2 x)}^{2} x} + 3 x \sqrt{9 x^{3}}$

Step 1.6

Pull terms out from under the radical.

$15 x^{2} \sqrt{x} - x (2 x \sqrt{x}) + 3 x \sqrt{9 x^{3}}$

Step 1.7

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

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Step 1.7.1

Move $x$ .

$15 x^{2} \sqrt{x} - (x \cdot x) (2 \sqrt{x}) + 3 x \sqrt{9 x^{3}}$

Step 1.7.2

Multiply $x$ by $x$ .

$15 x^{2} \sqrt{x} - x^{2} (2 \sqrt{x}) + 3 x \sqrt{9 x^{3}}$

Step 1.8

Multiply $2$ by $- 1$ .

$15 x^{2} \sqrt{x} - 2 x^{2} \sqrt{x} + 3 x \sqrt{9 x^{3}}$

Step 1.9

Rewrite $9 x^{3}$ as ${(3 x)}^{2} x$ .

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Step 1.9.1

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

$15 x^{2} \sqrt{x} - 2 x^{2} \sqrt{x} + 3 x \sqrt{3^{2} x^{3}}$

Step 1.9.2

Factor out $x^{2}$ .

$15 x^{2} \sqrt{x} - 2 x^{2} \sqrt{x} + 3 x \sqrt{3^{2} (x^{2} x)}$

Step 1.9.3

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

$15 x^{2} \sqrt{x} - 2 x^{2} \sqrt{x} + 3 x \sqrt{{(3 x)}^{2} x}$

Step 1.10

Pull terms out from under the radical.

$15 x^{2} \sqrt{x} - 2 x^{2} \sqrt{x} + 3 x (3 x \sqrt{x})$

Step 1.11

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

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Step 1.11.1

Move $x$ .

$15 x^{2} \sqrt{x} - 2 x^{2} \sqrt{x} + 3 (x \cdot x) (3 \sqrt{x})$

Step 1.11.2

Multiply $x$ by $x$ .

$15 x^{2} \sqrt{x} - 2 x^{2} \sqrt{x} + 3 x^{2} (3 \sqrt{x})$

Step 1.12

Multiply $3$ by $3$ .

$15 x^{2} \sqrt{x} - 2 x^{2} \sqrt{x} + 9 x^{2} \sqrt{x}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $2 x^{2} \sqrt{x}$ from $15 x^{2} \sqrt{x}$ .

$13 x^{2} \sqrt{x} + 9 x^{2} \sqrt{x}$

Step 2.2

Add $13 x^{2} \sqrt{x}$ and $9 x^{2} \sqrt{x}$ .

$22 x^{2} \sqrt{x}$