Solve (9+2sqrt{10})(9-2sqrt{10})

$$( 9 + 2 \sqrt { 10 } ) ( 9 - 2 \sqrt { 10 } )$$

Evaluate

$$41$$

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}.

$$9^{2}-\left(2\sqrt{10}\right)^{2}$$

Calculate 9 to the power of 2 and get 81.

$$81-\left(2\sqrt{10}\right)^{2}$$

Expand \left(2\sqrt{10}\right)^{2}.

$$81-2^{2}\left(\sqrt{10}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$81-4\left(\sqrt{10}\right)^{2}$$

The square of \sqrt{10} is 10.

$$81-4\times 10$$

Multiply 4 and 10 to get 40.

$$81-40$$

Subtract 40 from 81 to get 41.

$$41$$

Factor

$$41$$