Basic Math Examples

$2 y \sqrt{6 y w^{2}} - 8 w \sqrt{96 y^{5}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $6 y w^{2}$ as $w^{2} \cdot (6 y)$ .

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Step 1.1.1

Move $y$ .

$2 y \sqrt{6 w^{2} y} - 8 w \sqrt{96 y^{5}}$

Step 1.1.2

Reorder $6$ and $w^{2}$ .

$2 y \sqrt{w^{2} \cdot 6 y} - 8 w \sqrt{96 y^{5}}$

Step 1.1.3

Add parentheses.

$2 y \sqrt{w^{2} \cdot (6 y)} - 8 w \sqrt{96 y^{5}}$

Step 1.2

Pull terms out from under the radical.

$2 y (w \sqrt{6 y}) - 8 w \sqrt{96 y^{5}}$

Step 1.3

Rewrite $96 y^{5}$ as ${(4 y^{2})}^{2} \cdot (6 y)$ .

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Step 1.3.1

Factor $16$ out of $96$ .

$2 y (w \sqrt{6 y}) - 8 w \sqrt{16 (6) y^{5}}$

Step 1.3.2

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

$2 y (w \sqrt{6 y}) - 8 w \sqrt{4^{2} \cdot 6 y^{5}}$

Step 1.3.3

Factor out $y^{4}$ .

$2 y (w \sqrt{6 y}) - 8 w \sqrt{4^{2} \cdot 6 (y^{4} y)}$

Step 1.3.4

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

$2 y (w \sqrt{6 y}) - 8 w \sqrt{4^{2} \cdot 6 ({(y^{2})}^{2} y)}$

Step 1.3.5

Move $6$ .

$2 y (w \sqrt{6 y}) - 8 w \sqrt{4^{2} {(y^{2})}^{2} \cdot 6 y}$

Step 1.3.6

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

$2 y (w \sqrt{6 y}) - 8 w \sqrt{{(4 y^{2})}^{2} \cdot 6 y}$

Step 1.3.7

Add parentheses.

$2 y (w \sqrt{6 y}) - 8 w \sqrt{{(4 y^{2})}^{2} \cdot (6 y)}$

Step 1.4

Pull terms out from under the radical.

$2 y (w \sqrt{6 y}) - 8 w (4 y^{2} \sqrt{6 y})$

Step 1.5

Multiply $4$ by $- 8$ .

$2 y (w \sqrt{6 y}) - 32 w y^{2} \sqrt{6 y}$

Step 2

Reorder factors in $2 y (w \sqrt{6 y}) - 32 w y^{2} \sqrt{6 y}$ .

$2 y w \sqrt{6 y} - 32 w y^{2} \sqrt{6 y}$