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

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

Evaluate

$$1$$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Calculate 3 to the power of 2 and get 9.

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

Expand \left(2\sqrt{2}\right)^{2}.

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

Calculate 2 to the power of 2 and get 4.

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

The square of \sqrt{2} is 2.

$$9-4\times 2$$

Multiply 4 and 2 to get 8.

$$9-8$$

Subtract 8 from 9 to get 1.

$$1$$

Factor

$$1$$