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

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

Evaluate

$$24$$

Solution Steps

Use the distributive property to multiply 6 by \sqrt{6}+\sqrt{2}.

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

Apply the distributive property by multiplying each term of 6\sqrt{6}+6\sqrt{2} by each term of \sqrt{6}-\sqrt{2}.

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

The square of \sqrt{6} is 6.

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

Multiply 6 and 6 to get 36.

$$36-6\sqrt{6}\sqrt{2}+6\sqrt{2}\sqrt{6}-6\left(\sqrt{2}\right)^{2}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$36-6\sqrt{2}\sqrt{3}\sqrt{2}+6\sqrt{2}\sqrt{6}-6\left(\sqrt{2}\right)^{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$36-6\times 2\sqrt{3}+6\sqrt{2}\sqrt{6}-6\left(\sqrt{2}\right)^{2}$$

Multiply -6 and 2 to get -12.

$$36-12\sqrt{3}+6\sqrt{2}\sqrt{6}-6\left(\sqrt{2}\right)^{2}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$36-12\sqrt{3}+6\sqrt{2}\sqrt{2}\sqrt{3}-6\left(\sqrt{2}\right)^{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$36-12\sqrt{3}+6\times 2\sqrt{3}-6\left(\sqrt{2}\right)^{2}$$

Multiply 6 and 2 to get 12.

$$36-12\sqrt{3}+12\sqrt{3}-6\left(\sqrt{2}\right)^{2}$$

Combine -12\sqrt{3} and 12\sqrt{3} to get 0.

$$36-6\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$36-6\times 2$$

Multiply -6 and 2 to get -12.

$$36-12$$

Subtract 12 from 36 to get 24.

$$24$$

Factor

$$2^{3}\times 3$$