Solve -(sqrt{5}+sqrt{3})(sqrt{5}-sqrt{3})

$$- ( \sqrt { 5 } + \sqrt { 3 } ) ( \sqrt { 5 } - \sqrt { 3 } )$$

Evaluate

$$-2$$

Solution Steps

To find the opposite of \sqrt{5}+\sqrt{3}, find the opposite of each term.

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

Apply the distributive property by multiplying each term of -\sqrt{5}-\sqrt{3} by each term of \sqrt{5}-\sqrt{3}.

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

The square of \sqrt{5} is 5.

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

To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.

$$-5+\sqrt{15}-\sqrt{3}\sqrt{5}+\left(\sqrt{3}\right)^{2}$$

To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.

$$-5+\sqrt{15}-\sqrt{15}+\left(\sqrt{3}\right)^{2}$$

Combine \sqrt{15} and -\sqrt{15} to get 0.

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

The square of \sqrt{3} is 3.

$$-5+3$$

Add -5 and 3 to get -2.

$$-2$$

Factor

$$-2$$