Simplify 2 square root of 8x^2-5x square root of 32+5 square root of 18x^2

$2 \sqrt{8 x^{2}} - 5 x \sqrt{32} + 5 \sqrt{18 x^{2}}$

Step 1

Simplify each term.

Rewrite $8 x^{2}$ as ${(2 x)}^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$2 \sqrt{4 (2) x^{2}} - 5 x \sqrt{32} + 5 \sqrt{18 x^{2}}$

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

$2 \sqrt{2^{2} \cdot 2 x^{2}} - 5 x \sqrt{32} + 5 \sqrt{18 x^{2}}$

Move $2$ .

$2 \sqrt{2^{2} x^{2} \cdot 2} - 5 x \sqrt{32} + 5 \sqrt{18 x^{2}}$

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

$2 \sqrt{{(2 x)}^{2} \cdot 2} - 5 x \sqrt{32} + 5 \sqrt{18 x^{2}}$

Pull terms out from under the radical.

$2 (2 x \sqrt{2}) - 5 x \sqrt{32} + 5 \sqrt{18 x^{2}}$

Multiply $2$ by $2$ .

$4 (x \sqrt{2}) - 5 x \sqrt{32} + 5 \sqrt{18 x^{2}}$

Rewrite $32$ as $4^{2} \cdot 2$ .

Factor $16$ out of $32$ .

$4 x \sqrt{2} - 5 x \sqrt{16 (2)} + 5 \sqrt{18 x^{2}}$

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

$4 x \sqrt{2} - 5 x \sqrt{4^{2} \cdot 2} + 5 \sqrt{18 x^{2}}$

Pull terms out from under the radical.

$4 x \sqrt{2} - 5 x (4 \sqrt{2}) + 5 \sqrt{18 x^{2}}$

Multiply $4$ by $- 5$ .

$4 x \sqrt{2} - 20 x \sqrt{2} + 5 \sqrt{18 x^{2}}$

Rewrite $18 x^{2}$ as ${(3 x)}^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$4 x \sqrt{2} - 20 x \sqrt{2} + 5 \sqrt{9 (2) x^{2}}$

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

$4 x \sqrt{2} - 20 x \sqrt{2} + 5 \sqrt{3^{2} \cdot 2 x^{2}}$

Move $2$ .

$4 x \sqrt{2} - 20 x \sqrt{2} + 5 \sqrt{3^{2} x^{2} \cdot 2}$

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

$4 x \sqrt{2} - 20 x \sqrt{2} + 5 \sqrt{{(3 x)}^{2} \cdot 2}$

Pull terms out from under the radical.

$4 x \sqrt{2} - 20 x \sqrt{2} + 5 (3 x \sqrt{2})$

Multiply $3$ by $5$ .

$4 x \sqrt{2} - 20 x \sqrt{2} + 15 x \sqrt{2}$

Step 2

Simplify by adding terms.

Subtract $20 x \sqrt{2}$ from $4 x \sqrt{2}$ .

$- 16 x \sqrt{2} + 15 x \sqrt{2}$

Add $- 16 x \sqrt{2}$ and $15 x \sqrt{2}$ .

$- x \sqrt{2}$