Algebra Examples

$- 2 y \sqrt{28 x^{3}} + 3 x \sqrt{63 x y^{2}} - 3 \sqrt{112 x^{3} y^{2}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $28 x^{3}$ as ${(2 x)}^{2} \cdot (7 x)$ .

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Step 1.1.1

Factor $4$ out of $28$ .

$- 2 y \sqrt{4 (7) x^{3}} + 3 x \sqrt{63 x y^{2}} - 3 \sqrt{112 x^{3} y^{2}}$

Step 1.1.2

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

$- 2 y \sqrt{2^{2} \cdot 7 x^{3}} + 3 x \sqrt{63 x y^{2}} - 3 \sqrt{112 x^{3} y^{2}}$

Step 1.1.3

Factor out $x^{2}$ .

$- 2 y \sqrt{2^{2} \cdot 7 (x^{2} x)} + 3 x \sqrt{63 x y^{2}} - 3 \sqrt{112 x^{3} y^{2}}$

Step 1.1.4

Move $7$ .

$- 2 y \sqrt{2^{2} x^{2} \cdot 7 x} + 3 x \sqrt{63 x y^{2}} - 3 \sqrt{112 x^{3} y^{2}}$

Step 1.1.5

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

$- 2 y \sqrt{{(2 x)}^{2} \cdot 7 x} + 3 x \sqrt{63 x y^{2}} - 3 \sqrt{112 x^{3} y^{2}}$

Step 1.1.6

Add parentheses.

$- 2 y \sqrt{{(2 x)}^{2} \cdot (7 x)} + 3 x \sqrt{63 x y^{2}} - 3 \sqrt{112 x^{3} y^{2}}$

Step 1.2

Pull terms out from under the radical.

$- 2 y (2 x \sqrt{7 x}) + 3 x \sqrt{63 x y^{2}} - 3 \sqrt{112 x^{3} y^{2}}$

Step 1.3

Multiply $2$ by $- 2$ .

$- 4 y (x \sqrt{7 x}) + 3 x \sqrt{63 x y^{2}} - 3 \sqrt{112 x^{3} y^{2}}$

Step 1.4

Rewrite $63 x y^{2}$ as ${(3 y)}^{2} \cdot (7 x)$ .

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Step 1.4.1

Factor $9$ out of $63$ .

$- 4 y x \sqrt{7 x} + 3 x \sqrt{9 (7) x y^{2}} - 3 \sqrt{112 x^{3} y^{2}}$

Step 1.4.2

Rewrite $9$ as $3^{2}$ .

$- 4 y x \sqrt{7 x} + 3 x \sqrt{3^{2} \cdot 7 x y^{2}} - 3 \sqrt{112 x^{3} y^{2}}$

Step 1.4.3

Move $x$ .

$- 4 y x \sqrt{7 x} + 3 x \sqrt{3^{2} \cdot 7 y^{2} x} - 3 \sqrt{112 x^{3} y^{2}}$

Step 1.4.4

Move $7$ .

$- 4 y x \sqrt{7 x} + 3 x \sqrt{3^{2} y^{2} \cdot 7 x} - 3 \sqrt{112 x^{3} y^{2}}$

Step 1.4.5

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

$- 4 y x \sqrt{7 x} + 3 x \sqrt{{(3 y)}^{2} \cdot 7 x} - 3 \sqrt{112 x^{3} y^{2}}$

Step 1.4.6

Add parentheses.

$- 4 y x \sqrt{7 x} + 3 x \sqrt{{(3 y)}^{2} \cdot (7 x)} - 3 \sqrt{112 x^{3} y^{2}}$

Step 1.5

Pull terms out from under the radical.

$- 4 y x \sqrt{7 x} + 3 x (3 y \sqrt{7 x}) - 3 \sqrt{112 x^{3} y^{2}}$

Step 1.6

Multiply $3$ by $3$ .

$- 4 y x \sqrt{7 x} + 9 x (y \sqrt{7 x}) - 3 \sqrt{112 x^{3} y^{2}}$

Step 1.7

Rewrite $112 x^{3} y^{2}$ as ${(4 x y)}^{2} \cdot (7 x)$ .

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Step 1.7.1

Factor $16$ out of $112$ .

$- 4 y x \sqrt{7 x} + 9 x (y \sqrt{7 x}) - 3 \sqrt{16 (7) x^{3} y^{2}}$

Step 1.7.2

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

$- 4 y x \sqrt{7 x} + 9 x (y \sqrt{7 x}) - 3 \sqrt{4^{2} \cdot 7 x^{3} y^{2}}$

Step 1.7.3

Factor out $x^{2}$ .

$- 4 y x \sqrt{7 x} + 9 x (y \sqrt{7 x}) - 3 \sqrt{4^{2} \cdot 7 (x^{2} x) y^{2}}$

Step 1.7.4

Move $x$ .

$- 4 y x \sqrt{7 x} + 9 x (y \sqrt{7 x}) - 3 \sqrt{4^{2} \cdot 7 x^{2} y^{2} x}$

Step 1.7.5

Move $7$ .

$- 4 y x \sqrt{7 x} + 9 x (y \sqrt{7 x}) - 3 \sqrt{4^{2} x^{2} y^{2} \cdot 7 x}$

Step 1.7.6

Rewrite $(4^{2} (x^{2})) y^{2}$ as ${(4 x y)}^{2}$ .

$- 4 y x \sqrt{7 x} + 9 x (y \sqrt{7 x}) - 3 \sqrt{{(4 x y)}^{2} \cdot 7 x}$

Step 1.7.7

Add parentheses.

$- 4 y x \sqrt{7 x} + 9 x (y \sqrt{7 x}) - 3 \sqrt{{(4 x y)}^{2} \cdot (7 x)}$

Step 1.8

Pull terms out from under the radical.

$- 4 y x \sqrt{7 x} + 9 x (y \sqrt{7 x}) - 3 (4 x y \sqrt{7 x})$

Step 1.9

Multiply $4$ by $- 3$ .

$- 4 y x \sqrt{7 x} + 9 x (y \sqrt{7 x}) - 12 x y \sqrt{7 x}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $- 4 x y \sqrt{7 x}$ and $9 x y \sqrt{7 x}$ .

$5 x y \sqrt{7 x} - 12 x y \sqrt{7 x}$

Step 2.2

Subtract $12 x y \sqrt{7 x}$ from $5 x y \sqrt{7 x}$ .

$- 7 x y \sqrt{7 x}$