Algebra Examples

$2 (\sqrt[4]{16 x}) - 2 \sqrt[4]{2 y} + 3 (\sqrt[4]{81 x}) - 4 \sqrt[4]{32 y}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $16$ as $2^{4}$ .

$2 \sqrt[4]{2^{4} x} - 2 \sqrt[4]{2 y} + 3 (\sqrt[4]{81 x}) - 4 \sqrt[4]{32 y}$

Step 1.2

Pull terms out from under the radical.

$2 (2 \sqrt[4]{x}) - 2 \sqrt[4]{2 y} + 3 (\sqrt[4]{81 x}) - 4 \sqrt[4]{32 y}$

Step 1.3

Multiply $2$ by $2$ .

$4 \sqrt[4]{x} - 2 \sqrt[4]{2 y} + 3 (\sqrt[4]{81 x}) - 4 \sqrt[4]{32 y}$

Step 1.4

Rewrite $81$ as $3^{4}$ .

$4 \sqrt[4]{x} - 2 \sqrt[4]{2 y} + 3 \sqrt[4]{3^{4} x} - 4 \sqrt[4]{32 y}$

Step 1.5

Pull terms out from under the radical.

$4 \sqrt[4]{x} - 2 \sqrt[4]{2 y} + 3 (3 \sqrt[4]{x}) - 4 \sqrt[4]{32 y}$

Step 1.6

Multiply $3$ by $3$ .

$4 \sqrt[4]{x} - 2 \sqrt[4]{2 y} + 9 \sqrt[4]{x} - 4 \sqrt[4]{32 y}$

Step 1.7

Rewrite $32 y$ as $2^{4} \cdot (2 y)$ .

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Step 1.7.1

Factor $16$ out of $32$ .

$4 \sqrt[4]{x} - 2 \sqrt[4]{2 y} + 9 \sqrt[4]{x} - 4 \sqrt[4]{16 (2) y}$

Step 1.7.2

Rewrite $16$ as $2^{4}$ .

$4 \sqrt[4]{x} - 2 \sqrt[4]{2 y} + 9 \sqrt[4]{x} - 4 \sqrt[4]{2^{4} \cdot 2 y}$

Step 1.7.3

Add parentheses.

$4 \sqrt[4]{x} - 2 \sqrt[4]{2 y} + 9 \sqrt[4]{x} - 4 \sqrt[4]{2^{4} \cdot (2 y)}$

Step 1.8

Pull terms out from under the radical.

$4 \sqrt[4]{x} - 2 \sqrt[4]{2 y} + 9 \sqrt[4]{x} - 4 (2 \sqrt[4]{2 y})$

Step 1.9

Multiply $2$ by $- 4$ .

$4 \sqrt[4]{x} - 2 \sqrt[4]{2 y} + 9 \sqrt[4]{x} - 8 \sqrt[4]{2 y}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $4 \sqrt[4]{x}$ and $9 \sqrt[4]{x}$ .

$13 \sqrt[4]{x} - 2 \sqrt[4]{2 y} - 8 \sqrt[4]{2 y}$

Step 2.2

Subtract $8 \sqrt[4]{2 y}$ from $- 2 \sqrt[4]{2 y}$ .

$13 \sqrt[4]{x} - 10 \sqrt[4]{2 y}$