Basic Math Examples

$2 \sqrt[3]{16 p^{3} y^{4}} + 4 p \sqrt[3]{54 y^{4}} - 3 y \sqrt[3]{16 p^{3} y}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $16 p^{3} y^{4}$ as ${(2 p y)}^{3} \cdot (2 y)$ .

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Step 1.1.1

Factor $8$ out of $16$ .

$2 \sqrt[3]{8 (2) p^{3} y^{4}} + 4 p \sqrt[3]{54 y^{4}} - 3 y \sqrt[3]{16 p^{3} y}$

Step 1.1.2

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

$2 \sqrt[3]{2^{3} \cdot 2 p^{3} y^{4}} + 4 p \sqrt[3]{54 y^{4}} - 3 y \sqrt[3]{16 p^{3} y}$

Step 1.1.3

Factor out $y^{3}$ .

$2 \sqrt[3]{2^{3} \cdot 2 p^{3} (y^{3} y)} + 4 p \sqrt[3]{54 y^{4}} - 3 y \sqrt[3]{16 p^{3} y}$

Step 1.1.4

Move $2$ .

$2 \sqrt[3]{2^{3} p^{3} y^{3} \cdot 2 y} + 4 p \sqrt[3]{54 y^{4}} - 3 y \sqrt[3]{16 p^{3} y}$

Step 1.1.5

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

$2 \sqrt[3]{{(2 p y)}^{3} \cdot 2 y} + 4 p \sqrt[3]{54 y^{4}} - 3 y \sqrt[3]{16 p^{3} y}$

Step 1.1.6

Add parentheses.

$2 \sqrt[3]{{(2 p y)}^{3} \cdot (2 y)} + 4 p \sqrt[3]{54 y^{4}} - 3 y \sqrt[3]{16 p^{3} y}$

Step 1.2

Pull terms out from under the radical.

$2 (2 p y \sqrt[3]{2 y}) + 4 p \sqrt[3]{54 y^{4}} - 3 y \sqrt[3]{16 p^{3} y}$

Step 1.3

Multiply $2$ by $2$ .

$4 (p y \sqrt[3]{2 y}) + 4 p \sqrt[3]{54 y^{4}} - 3 y \sqrt[3]{16 p^{3} y}$

Step 1.4

Rewrite $54 y^{4}$ as ${(3 y)}^{3} \cdot (2 y)$ .

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Step 1.4.1

Factor $27$ out of $54$ .

$4 p y \sqrt[3]{2 y} + 4 p \sqrt[3]{27 (2) y^{4}} - 3 y \sqrt[3]{16 p^{3} y}$

Step 1.4.2

Rewrite $27$ as $3^{3}$ .

$4 p y \sqrt[3]{2 y} + 4 p \sqrt[3]{3^{3} \cdot 2 y^{4}} - 3 y \sqrt[3]{16 p^{3} y}$

Step 1.4.3

Factor out $y^{3}$ .

$4 p y \sqrt[3]{2 y} + 4 p \sqrt[3]{3^{3} \cdot 2 (y^{3} y)} - 3 y \sqrt[3]{16 p^{3} y}$

Step 1.4.4

Move $2$ .

$4 p y \sqrt[3]{2 y} + 4 p \sqrt[3]{3^{3} y^{3} \cdot 2 y} - 3 y \sqrt[3]{16 p^{3} y}$

Step 1.4.5

Rewrite $3^{3} y^{3}$ as ${(3 y)}^{3}$ .

$4 p y \sqrt[3]{2 y} + 4 p \sqrt[3]{{(3 y)}^{3} \cdot 2 y} - 3 y \sqrt[3]{16 p^{3} y}$

Step 1.4.6

Add parentheses.

$4 p y \sqrt[3]{2 y} + 4 p \sqrt[3]{{(3 y)}^{3} \cdot (2 y)} - 3 y \sqrt[3]{16 p^{3} y}$

Step 1.5

Pull terms out from under the radical.

$4 p y \sqrt[3]{2 y} + 4 p (3 y \sqrt[3]{2 y}) - 3 y \sqrt[3]{16 p^{3} y}$

Step 1.6

Multiply $3$ by $4$ .

$4 p y \sqrt[3]{2 y} + 12 p (y \sqrt[3]{2 y}) - 3 y \sqrt[3]{16 p^{3} y}$

Step 1.7

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

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Step 1.7.1

Factor $8$ out of $16$ .

$4 p y \sqrt[3]{2 y} + 12 p y \sqrt[3]{2 y} - 3 y \sqrt[3]{8 (2) p^{3} y}$

Step 1.7.2

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

$4 p y \sqrt[3]{2 y} + 12 p y \sqrt[3]{2 y} - 3 y \sqrt[3]{2^{3} \cdot 2 p^{3} y}$

Step 1.7.3

Move $2$ .

$4 p y \sqrt[3]{2 y} + 12 p y \sqrt[3]{2 y} - 3 y \sqrt[3]{2^{3} p^{3} \cdot 2 y}$

Step 1.7.4

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

$4 p y \sqrt[3]{2 y} + 12 p y \sqrt[3]{2 y} - 3 y \sqrt[3]{{(2 p)}^{3} \cdot 2 y}$

Step 1.7.5

Add parentheses.

$4 p y \sqrt[3]{2 y} + 12 p y \sqrt[3]{2 y} - 3 y \sqrt[3]{{(2 p)}^{3} \cdot (2 y)}$

Step 1.8

Pull terms out from under the radical.

$4 p y \sqrt[3]{2 y} + 12 p y \sqrt[3]{2 y} - 3 y (2 p \sqrt[3]{2 y})$

Step 1.9

Multiply $2$ by $- 3$ .

$4 p y \sqrt[3]{2 y} + 12 p y \sqrt[3]{2 y} - 6 y (p \sqrt[3]{2 y})$

Step 2

Add $4 p y \sqrt[3]{2 y}$ and $12 p y \sqrt[3]{2 y}$ .

$16 p y \sqrt[3]{2 y} - 6 y (p \sqrt[3]{2 y})$

Step 3

Subtract $6 y (p \sqrt[3]{2 y})$ from $16 p y \sqrt[3]{2 y}$ .

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Step 3.1

Move $y$ .

$16 p y \sqrt[3]{2 y} - 6 p y \sqrt[3]{2 y}$

Step 3.2

Subtract $6 p y \sqrt[3]{2 y}$ from $16 p y \sqrt[3]{2 y}$ .

$10 p y \sqrt[3]{2 y}$