Simplify the Radical Expression -2y square root of 28x^3+3x square root of 63xy^2-3 square root of 112x^3y^2

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

Step 1

Simplify each term.

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

Factor $4$ out of $28$ .

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

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

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

Factor out $x^{2}$ .

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

Move $7$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Remove non-negative terms from the absolute value.

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

Multiply $2$ by $- 2$ .

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

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

Factor $9$ out of $63$ .

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

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

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

Move $x$ .

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

Move $7$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Remove non-negative terms from the absolute value.

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

Multiply $3$ by $3$ .

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

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

Factor $16$ out of $112$ .

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

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

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

Factor out $x^{2}$ .

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

Move $x$ .

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

Move $7$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Remove non-negative terms from the absolute value.

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

Multiply $4$ by $- 3$ .

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

Step 2

Reorder factors in $- 4 y | x | \sqrt{7 x} + 9 x (| y | \sqrt{7 x}) - 12 | x y | \sqrt{7 x}$ .

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

Simplify the Radical Expression -2y square root of 28x^3+3x square root of 63xy^2-3 square root of 112x^3y^2

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