Linear Algebra Examples

$4 w \sqrt{27 w y^{2}} - y \sqrt{12 w^{3}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $27 w y^{2}$ as ${(3 y)}^{2} \cdot (3 w)$ .

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Step 1.1.1

Factor $9$ out of $27$ .

$4 w \sqrt{9 (3) w y^{2}} - y \sqrt{12 w^{3}}$

Step 1.1.2

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

$4 w \sqrt{3^{2} \cdot 3 w y^{2}} - y \sqrt{12 w^{3}}$

Step 1.1.3

Move $w$ .

$4 w \sqrt{3^{2} \cdot 3 y^{2} w} - y \sqrt{12 w^{3}}$

Step 1.1.4

Move $3$ .

$4 w \sqrt{3^{2} y^{2} \cdot 3 w} - y \sqrt{12 w^{3}}$

Step 1.1.5

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

$4 w \sqrt{{(3 y)}^{2} \cdot 3 w} - y \sqrt{12 w^{3}}$

Step 1.1.6

Add parentheses.

$4 w \sqrt{{(3 y)}^{2} \cdot (3 w)} - y \sqrt{12 w^{3}}$

Step 1.2

Pull terms out from under the radical.

$4 w (3 y \sqrt{3 w}) - y \sqrt{12 w^{3}}$

Step 1.3

Multiply $3$ by $4$ .

$12 w (y \sqrt{3 w}) - y \sqrt{12 w^{3}}$

Step 1.4

Rewrite $12 w^{3}$ as ${(2 w)}^{2} \cdot (3 w)$ .

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Step 1.4.1

Factor $4$ out of $12$ .

$12 w (y \sqrt{3 w}) - y \sqrt{4 (3) w^{3}}$

Step 1.4.2

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

$12 w (y \sqrt{3 w}) - y \sqrt{2^{2} \cdot 3 w^{3}}$

Step 1.4.3

Factor out $w^{2}$ .

$12 w (y \sqrt{3 w}) - y \sqrt{2^{2} \cdot 3 (w^{2} w)}$

Step 1.4.4

Move $3$ .

$12 w (y \sqrt{3 w}) - y \sqrt{2^{2} w^{2} \cdot 3 w}$

Step 1.4.5

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

$12 w (y \sqrt{3 w}) - y \sqrt{{(2 w)}^{2} \cdot 3 w}$

Step 1.4.6

Add parentheses.

$12 w (y \sqrt{3 w}) - y \sqrt{{(2 w)}^{2} \cdot (3 w)}$

Step 1.5

Pull terms out from under the radical.

$12 w (y \sqrt{3 w}) - y (2 w \sqrt{3 w})$

Step 1.6

Multiply $2$ by $- 1$ .

$12 w (y \sqrt{3 w}) - 2 y w \sqrt{3 w}$

Step 2

Simplify by adding terms.

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Step 2.1

Move $y$ .

$12 w y \sqrt{3 w} - 2 w y \sqrt{3 w}$

Step 2.2

Subtract $2 w y \sqrt{3 w}$ from $12 w y \sqrt{3 w}$ .

$10 w y \sqrt{3 w}$