Solve (3sqrt{5}-2sqrt{6})(3sqrt{5}+2sqrt{6})=

$$( 3 \sqrt { 5 } - 2 \sqrt { 6 } ) ( 3 \sqrt { 5 } + 2 \sqrt { 6 } ) =$$

Evaluate

$$21$$

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}.

$$\left(3\sqrt{5}\right)^{2}-\left(2\sqrt{6}\right)^{2}$$

Expand \left(3\sqrt{5}\right)^{2}.

$$3^{2}\left(\sqrt{5}\right)^{2}-\left(2\sqrt{6}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9\left(\sqrt{5}\right)^{2}-\left(2\sqrt{6}\right)^{2}$$

The square of \sqrt{5} is 5.

$$9\times 5-\left(2\sqrt{6}\right)^{2}$$

Multiply 9 and 5 to get 45.

$$45-\left(2\sqrt{6}\right)^{2}$$

Expand \left(2\sqrt{6}\right)^{2}.

$$45-2^{2}\left(\sqrt{6}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$45-4\left(\sqrt{6}\right)^{2}$$

The square of \sqrt{6} is 6.

$$45-4\times 6$$

Multiply 4 and 6 to get 24.

$$45-24$$

Subtract 24 from 45 to get 21.

$$21$$

Factor

$$3\times 7$$