Simplify ( square root of 2+3)( square root of 2-3)x^2

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

Expand $(\sqrt{2} + 3) (\sqrt{2} - 3)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Combine using the product rule for radicals.

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

Multiply $2$ by $2$ .

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

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

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

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

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

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

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

Multiply $3$ by $- 3$ .

$(2 - 3 \sqrt{2} + 3 \sqrt{2} - 9) x^{2}$

Subtract $9$ from $2$ .

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

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

$(- 7 + 0) x^{2}$

Add $- 7$ and $0$ .

$- 7 x^{2}$