Simplify 7 square root of 2x^4-x^2 square root of 18

$7 \sqrt{2 x^{4}} - x^{2} \sqrt{18}$

Simplify each term.

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

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

$7 \sqrt{2 {(x^{2})}^{2}} - x^{2} \sqrt{18}$

Reorder $2$ and ${(x^{2})}^{2}$ .

$7 \sqrt{{(x^{2})}^{2} \cdot 2} - x^{2} \sqrt{18}$

Pull terms out from under the radical.

$7 (x^{2} \sqrt{2}) - x^{2} \sqrt{18}$

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

Factor $9$ out of $18$ .

$7 x^{2} \sqrt{2} - x^{2} \sqrt{9 (2)}$

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

$7 x^{2} \sqrt{2} - x^{2} \sqrt{3^{2} \cdot 2}$

Pull terms out from under the radical.

$7 x^{2} \sqrt{2} - x^{2} (3 \sqrt{2})$

Multiply $3$ by $- 1$ .

$7 x^{2} \sqrt{2} - 3 x^{2} \sqrt{2}$

Subtract $3 x^{2} \sqrt{2}$ from $7 x^{2} \sqrt{2}$ .

$4 x^{2} \sqrt{2}$