Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

Pull terms out from under the radical.

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

Step 1.3

Multiply $5$ by $3$ .

$15 x \sqrt{x} - 9 x \sqrt{4 x} - 3 x \sqrt{x}$

Step 1.4

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

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

Step 1.5

Pull terms out from under the radical.

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

Step 1.6

Multiply $2$ by $- 9$ .

$15 x \sqrt{x} - 18 x \sqrt{x} - 3 x \sqrt{x}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $18 x \sqrt{x}$ from $15 x \sqrt{x}$ .

$- 3 x \sqrt{x} - 3 x \sqrt{x}$

Step 2.2

Subtract $3 x \sqrt{x}$ from $- 3 x \sqrt{x}$ .

$- 6 x \sqrt{x}$