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

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

Evaluate

$$17$$

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}.

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

Calculate 5 to the power of 2 and get 25.

$$25-\left(2\sqrt{2}\right)^{2}$$

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

$$25-2^{2}\left(\sqrt{2}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$25-4\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$25-4\times 2$$

Multiply 4 and 2 to get 8.

$$25-8$$

Subtract 8 from 25 to get 17.

$$17$$

Factor

$$17$$