Solve (3sqrt{6}-4sqrt{2})(3sqrt{6}+4sqrt{2})

$$( 3 \sqrt { 6 } - 4 \sqrt { 2 } ) ( 3 \sqrt { 6 } + 4 \sqrt { 2 } )$$

Evaluate

$$22$$

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}.

$$\left(3\sqrt{6}\right)^{2}-\left(4\sqrt{2}\right)^{2}$$

Expand \left(3\sqrt{6}\right)^{2}.

$$3^{2}\left(\sqrt{6}\right)^{2}-\left(4\sqrt{2}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9\left(\sqrt{6}\right)^{2}-\left(4\sqrt{2}\right)^{2}$$

The square of \sqrt{6} is 6.

$$9\times 6-\left(4\sqrt{2}\right)^{2}$$

Multiply 9 and 6 to get 54.

$$54-\left(4\sqrt{2}\right)^{2}$$

Expand \left(4\sqrt{2}\right)^{2}.

$$54-4^{2}\left(\sqrt{2}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$54-16\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$54-16\times 2$$

Multiply 16 and 2 to get 32.

$$54-32$$

Subtract 32 from 54 to get 22.

$$22$$

Factor

$$2\times 11$$