Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

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

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

Step 1.1.2

Factor out $x^{2}$ .

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

Step 1.1.3

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

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

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

Step 1.2

Pull terms out from under the radical.

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

Step 1.3

Rewrite using the commutative property of multiplication.

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

Step 1.4

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

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Step 1.4.1

Move $x$ .

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

Step 1.4.2

Multiply $x$ by $x$ .

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

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

Step 1.5

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

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Step 1.5.1

Factor out $x^{4}$ .

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

Step 1.5.2

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

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

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

Step 1.6

Pull terms out from under the radical.

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

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

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $2 x^{2} \sqrt{x}$ from $3 x^{2} \sqrt{x}$ .

$1 x^{2} \sqrt{x}$

Step 2.2

Multiply $x^{2}$ by $1$ .

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

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

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