Algebra Examples

$\sqrt[3]{x^{5}} - 2 \sqrt[3]{x^{7}} - \sqrt[3]{x^{8}}$

Step 1

Factor out $x^{3}$ .

$\sqrt[3]{x^{3} x^{2}} - 2 \sqrt[3]{x^{7}} - \sqrt[3]{x^{8}}$

Step 2

Pull terms out from under the radical.

$x \sqrt[3]{x^{2}} - 2 \sqrt[3]{x^{7}} - \sqrt[3]{x^{8}}$

Step 3

Rewrite $x^{7}$ as ${(x^{2})}^{3} x$ .

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Step 3.1

Factor out $x^{6}$ .

$x \sqrt[3]{x^{2}} - 2 \sqrt[3]{x^{6} x} - \sqrt[3]{x^{8}}$

Step 3.2

Rewrite $x^{6}$ as ${(x^{2})}^{3}$ .

$x \sqrt[3]{x^{2}} - 2 \sqrt[3]{{(x^{2})}^{3} x} - \sqrt[3]{x^{8}}$

Step 4

Pull terms out from under the radical.

$x \sqrt[3]{x^{2}} - 2 (x^{2} \sqrt[3]{x}) - \sqrt[3]{x^{8}}$

Step 5

Rewrite $x^{8}$ as ${(x^{2})}^{3} x^{2}$ .

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Step 5.1

Factor out $x^{6}$ .

$x \sqrt[3]{x^{2}} - 2 x^{2} \sqrt[3]{x} - \sqrt[3]{x^{6} x^{2}}$

Step 5.2

Rewrite $x^{6}$ as ${(x^{2})}^{3}$ .

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

Step 6

Pull terms out from under the radical.

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