Solve (3sqrt{2}+2sqrt{5})*(3sqrt{2}-2sqrt{5})

$$( 3 \sqrt { 2 } + 2 \sqrt { 5 } ) \cdot ( 3 \sqrt { 2 } - 2 \sqrt { 5 } )$$

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}.

$$\left(3\sqrt{2}\right)^{2}-\left(2\sqrt{5}\right)^{2}$$

Expand \left(3\sqrt{2}\right)^{2}.

$$3^{2}\left(\sqrt{2}\right)^{2}-\left(2\sqrt{5}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9\left(\sqrt{2}\right)^{2}-\left(2\sqrt{5}\right)^{2}$$

The square of \sqrt{2} is 2.

$$9\times 2-\left(2\sqrt{5}\right)^{2}$$

Multiply 9 and 2 to get 18.

$$18-\left(2\sqrt{5}\right)^{2}$$

Expand \left(2\sqrt{5}\right)^{2}.

$$18-2^{2}\left(\sqrt{5}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$18-4\left(\sqrt{5}\right)^{2}$$

The square of \sqrt{5} is 5.

$$18-4\times 5$$

Multiply 4 and 5 to get 20.

$$18-20$$

Subtract 20 from 18 to get -2.

$$-2$$

Factor

$$-2$$