Algebra Examples

$12 \sqrt[3]{16 x y} - 5 \sqrt[3]{8 x y} + 12 \sqrt[3]{2 x y}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $16 x y$ as $2^{3} \cdot (2 x y)$ .

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Step 1.1.1

Factor $8$ out of $16$ .

$12 \sqrt[3]{8 (2) x y} - 5 \sqrt[3]{8 x y} + 12 \sqrt[3]{2 x y}$

Step 1.1.2

Rewrite $8$ as $2^{3}$ .

$12 \sqrt[3]{2^{3} \cdot 2 x y} - 5 \sqrt[3]{8 x y} + 12 \sqrt[3]{2 x y}$

Step 1.1.3

Add parentheses.

$12 \sqrt[3]{2^{3} \cdot 2 (x y)} - 5 \sqrt[3]{8 x y} + 12 \sqrt[3]{2 x y}$

Step 1.1.4

Add parentheses.

$12 \sqrt[3]{2^{3} \cdot (2 x y)} - 5 \sqrt[3]{8 x y} + 12 \sqrt[3]{2 x y}$

Step 1.2

Pull terms out from under the radical.

$12 (2 \sqrt[3]{2 x y}) - 5 \sqrt[3]{8 x y} + 12 \sqrt[3]{2 x y}$

Step 1.3

Multiply $2$ by $12$ .

$24 \sqrt[3]{2 x y} - 5 \sqrt[3]{8 x y} + 12 \sqrt[3]{2 x y}$

Step 1.4

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

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Step 1.4.1

Rewrite $8$ as $2^{3}$ .

$24 \sqrt[3]{2 x y} - 5 \sqrt[3]{2^{3} x y} + 12 \sqrt[3]{2 x y}$

Step 1.4.2

Add parentheses.

$24 \sqrt[3]{2 x y} - 5 \sqrt[3]{2^{3} (x y)} + 12 \sqrt[3]{2 x y}$

Step 1.5

Pull terms out from under the radical.

$24 \sqrt[3]{2 x y} - 5 (2 \sqrt[3]{x y}) + 12 \sqrt[3]{2 x y}$

Step 1.6

Multiply $2$ by $- 5$ .

$24 \sqrt[3]{2 x y} - 10 \sqrt[3]{x y} + 12 \sqrt[3]{2 x y}$

Step 2

Add $24 \sqrt[3]{2 x y}$ and $12 \sqrt[3]{2 x y}$ .

$36 \sqrt[3]{2 x y} - 10 \sqrt[3]{x y}$