Solve (3+2sqrt{2})(3-2sqrt{2})(3+2sqrt{2}-3+2sqrt{2}=

$$(3+2 \sqrt{ 2 } )(3-2 \sqrt{ 2 } )(3+2 \sqrt{ 2 } -3+2 \sqrt{ 2 } =$$

Evaluate

$$4\sqrt{2}\approx 5.656854249$$

Solution Steps

Subtract 3 from 3 to get 0.

$$\left(3+2\sqrt{2}\right)\left(3-2\sqrt{2}\right)\left(2\sqrt{2}+2\sqrt{2}\right)$$

Combine 2\sqrt{2} and 2\sqrt{2} to get 4\sqrt{2}.

$$\left(3+2\sqrt{2}\right)\left(3-2\sqrt{2}\right)\times 4\sqrt{2}$$

Apply the distributive property by multiplying each term of 3+2\sqrt{2} by each term of 3-2\sqrt{2}.

$$\left(9-6\sqrt{2}+6\sqrt{2}-4\left(\sqrt{2}\right)^{2}\right)\times 4\sqrt{2}$$

Combine -6\sqrt{2} and 6\sqrt{2} to get 0.

$$\left(9-4\left(\sqrt{2}\right)^{2}\right)\times 4\sqrt{2}$$

The square of \sqrt{2} is 2.

$$\left(9-4\times 2\right)\times 4\sqrt{2}$$

Multiply -4 and 2 to get -8.

$$\left(9-8\right)\times 4\sqrt{2}$$

Subtract 8 from 9 to get 1.

$$1\times 4\sqrt{2}$$

Multiply 1 and 4 to get 4.

$$4\sqrt{2}$$