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

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

Evaluate

$$-48$$

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}.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

The square of \sqrt{6} is 6.

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

Multiply 4 and 6 to get 24.

$$24-\left(6\sqrt{2}\right)^{2}$$

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

$$24-6^{2}\left(\sqrt{2}\right)^{2}$$

Calculate 6 to the power of 2 and get 36.

$$24-36\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$24-36\times 2$$

Multiply 36 and 2 to get 72.

$$24-72$$

Subtract 72 from 24 to get -48.

$$-48$$

Factor

$$-48$$