Solve (sqrt{5}+2sqrt{2})*(sqrt{5}-2sqrt{2})=

$$( \sqrt{ 5 } +2 \sqrt{ 2 } ) \times ( \sqrt{ 5 } -2 \sqrt{ 2 } )=$$

Evaluate

$$-3$$

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}.

$$\left(\sqrt{5}\right)^{2}-\left(2\sqrt{2}\right)^{2}$$

The square of \sqrt{5} is 5.

$$5-\left(2\sqrt{2}\right)^{2}$$

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

$$5-2^{2}\left(\sqrt{2}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$5-4\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$5-4\times 2$$

Multiply 4 and 2 to get 8.

$$5-8$$

Subtract 8 from 5 to get -3.

$$-3$$

Factor

$$-3$$