Solve (sqrt{10}-2sqrt{2})(sqrt{10}+2sqrt{2})

$$( \sqrt { 10 } - 2 \sqrt { 2 } ) ( \sqrt { 10 } + 2 \sqrt { 2 } )$$

Evaluate

$$2$$

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}.

$$\left(\sqrt{10}\right)^{2}-\left(2\sqrt{2}\right)^{2}$$

The square of \sqrt{10} is 10.

$$10-\left(2\sqrt{2}\right)^{2}$$

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

$$10-2^{2}\left(\sqrt{2}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$10-4\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$10-4\times 2$$

Multiply 4 and 2 to get 8.

$$10-8$$

Subtract 8 from 10 to get 2.

$$2$$

Factor

$$2$$