Simplify 9-3 square root of 2+ square root of 2*3- square root of 2^2

$9 - 3 \sqrt{2} + \sqrt{2} \cdot 3 - \sqrt{2^{2}}$

Simplify each term.

Move $3$ to the left of $\sqrt{2}$ .

$9 - 3 \sqrt{2} + 3 \cdot \sqrt{2} - \sqrt{2^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$9 - 3 \sqrt{2} + 3 \sqrt{2} - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$9 - 3 \sqrt{2} + 3 \sqrt{2} - 2$

Simplify by adding terms.

Subtract $2$ from $9$ .

$7 - 3 \sqrt{2} + 3 \sqrt{2}$

Add $- 3 \sqrt{2}$ and $3 \sqrt{2}$ .

$7 + 0$

Add $7$ and $0$ .

$7$