Algebra Examples

$8 \sqrt{14 x^{3} y^{2}} - 4 \sqrt{14 x^{3} y^{2}} + 2 x \sqrt[3]{6 x^{4} y^{4}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $14 x^{3} y^{2}$ as ${(x y)}^{2} \cdot (14 x)$ .

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Step 1.1.1

Factor out $x^{2}$ .

$8 \sqrt{14 (x^{2} x) y^{2}} - 4 \sqrt{14 x^{3} y^{2}} + 2 x \sqrt[3]{6 x^{4} y^{4}}$

Step 1.1.2

Move $x$ .

$8 \sqrt{14 (x^{2}) y^{2} x} - 4 \sqrt{14 x^{3} y^{2}} + 2 x \sqrt[3]{6 x^{4} y^{4}}$

Step 1.1.3

Move $14$ .

$8 \sqrt{(x^{2}) y^{2} \cdot 14 x} - 4 \sqrt{14 x^{3} y^{2}} + 2 x \sqrt[3]{6 x^{4} y^{4}}$

Step 1.1.4

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

$8 \sqrt{{(x y)}^{2} \cdot 14 x} - 4 \sqrt{14 x^{3} y^{2}} + 2 x \sqrt[3]{6 x^{4} y^{4}}$

Step 1.1.5

Add parentheses.

$8 \sqrt{{(x y)}^{2} \cdot (14 x)} - 4 \sqrt{14 x^{3} y^{2}} + 2 x \sqrt[3]{6 x^{4} y^{4}}$

Step 1.2

Pull terms out from under the radical.

$8 (x y \sqrt{14 x}) - 4 \sqrt{14 x^{3} y^{2}} + 2 x \sqrt[3]{6 x^{4} y^{4}}$

Step 1.3

Rewrite $14 x^{3} y^{2}$ as ${(x y)}^{2} \cdot (14 x)$ .

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Step 1.3.1

Factor out $x^{2}$ .

$8 x y \sqrt{14 x} - 4 \sqrt{14 (x^{2} x) y^{2}} + 2 x \sqrt[3]{6 x^{4} y^{4}}$

Step 1.3.2

Move $x$ .

$8 x y \sqrt{14 x} - 4 \sqrt{14 (x^{2}) y^{2} x} + 2 x \sqrt[3]{6 x^{4} y^{4}}$

Step 1.3.3

Move $14$ .

$8 x y \sqrt{14 x} - 4 \sqrt{(x^{2}) y^{2} \cdot 14 x} + 2 x \sqrt[3]{6 x^{4} y^{4}}$

Step 1.3.4

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

$8 x y \sqrt{14 x} - 4 \sqrt{{(x y)}^{2} \cdot 14 x} + 2 x \sqrt[3]{6 x^{4} y^{4}}$

Step 1.3.5

Add parentheses.

$8 x y \sqrt{14 x} - 4 \sqrt{{(x y)}^{2} \cdot (14 x)} + 2 x \sqrt[3]{6 x^{4} y^{4}}$

Step 1.4

Pull terms out from under the radical.

$8 x y \sqrt{14 x} - 4 (x y \sqrt{14 x}) + 2 x \sqrt[3]{6 x^{4} y^{4}}$

Step 1.5

Rewrite $6 x^{4} y^{4}$ as ${(x y)}^{3} \cdot (6 x y)$ .

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Step 1.5.1

Factor out $x^{3}$ .

$8 x y \sqrt{14 x} - 4 x y \sqrt{14 x} + 2 x \sqrt[3]{6 (x^{3} x) y^{4}}$

Step 1.5.2

Factor out $y^{3}$ .

$8 x y \sqrt{14 x} - 4 x y \sqrt{14 x} + 2 x \sqrt[3]{6 (x^{3} x) (y^{3} y)}$

Step 1.5.3

Move $x$ .

$8 x y \sqrt{14 x} - 4 x y \sqrt{14 x} + 2 x \sqrt[3]{6 (x^{3}) y^{3} x y}$

Step 1.5.4

Move $6$ .

$8 x y \sqrt{14 x} - 4 x y \sqrt{14 x} + 2 x \sqrt[3]{(x^{3}) y^{3} \cdot 6 x y}$

Step 1.5.5

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

$8 x y \sqrt{14 x} - 4 x y \sqrt{14 x} + 2 x \sqrt[3]{{(x y)}^{3} \cdot 6 x y}$

Step 1.5.6

Add parentheses.

$8 x y \sqrt{14 x} - 4 x y \sqrt{14 x} + 2 x \sqrt[3]{{(x y)}^{3} \cdot 6 (x y)}$

Step 1.5.7

Add parentheses.

$8 x y \sqrt{14 x} - 4 x y \sqrt{14 x} + 2 x \sqrt[3]{{(x y)}^{3} \cdot (6 x y)}$

Step 1.6

Pull terms out from under the radical.

$8 x y \sqrt{14 x} - 4 x y \sqrt{14 x} + 2 x (x y \sqrt[3]{6 x y})$

Step 1.7

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

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Step 1.7.1

Move $x$ .

$8 x y \sqrt{14 x} - 4 x y \sqrt{14 x} + 2 (x \cdot x) (y \sqrt[3]{6 x y})$

Step 1.7.2

Multiply $x$ by $x$ .

$8 x y \sqrt{14 x} - 4 x y \sqrt{14 x} + 2 x^{2} (y \sqrt[3]{6 x y})$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $4 x y \sqrt{14 x}$ from $8 x y \sqrt{14 x}$ .

$4 x y \sqrt{14 x} + 2 x^{2} (y \sqrt[3]{6 x y})$

Step 2.2

Reorder factors in $4 x y \sqrt{14 x} + 2 x^{2} (y \sqrt[3]{6 x y})$ .

$4 x y \sqrt{14 x} + 2 x^{2} y \sqrt[3]{6 x y}$