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

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

Evaluate

$$-78$$

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}.

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

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

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

Calculate 3 to the power of 2 and get 9.

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

The square of \sqrt{2} is 2.

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

Multiply 9 and 2 to get 18.

$$18-\left(4\sqrt{6}\right)^{2}$$

Expand \left(4\sqrt{6}\right)^{2}.

$$18-4^{2}\left(\sqrt{6}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$18-16\left(\sqrt{6}\right)^{2}$$

The square of \sqrt{6} is 6.

$$18-16\times 6$$

Multiply 16 and 6 to get 96.

$$18-96$$

Subtract 96 from 18 to get -78.

$$-78$$

Factor

$$-78$$