Solve (4)(sqrt{3}-sqrt{5})(sqrt{5}+sqrt{3})=

$$( 4 ) ( \sqrt { 3 } - \sqrt { 5 } ) ( \sqrt { 5 } + \sqrt { 3 } ) =$$

Evaluate

$$-8$$

Solution Steps

Use the distributive property to multiply 4 by \sqrt{3}-\sqrt{5}.

$$\left(4\sqrt{3}-4\sqrt{5}\right)\left(\sqrt{5}+\sqrt{3}\right)$$

Apply the distributive property by multiplying each term of 4\sqrt{3}-4\sqrt{5} by each term of \sqrt{5}+\sqrt{3}.

$$4\sqrt{3}\sqrt{5}+4\left(\sqrt{3}\right)^{2}-4\left(\sqrt{5}\right)^{2}-4\sqrt{5}\sqrt{3}$$

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

$$4\sqrt{15}+4\left(\sqrt{3}\right)^{2}-4\left(\sqrt{5}\right)^{2}-4\sqrt{5}\sqrt{3}$$

The square of \sqrt{3} is 3.

$$4\sqrt{15}+4\times 3-4\left(\sqrt{5}\right)^{2}-4\sqrt{5}\sqrt{3}$$

Multiply 4 and 3 to get 12.

$$4\sqrt{15}+12-4\left(\sqrt{5}\right)^{2}-4\sqrt{5}\sqrt{3}$$

The square of \sqrt{5} is 5.

$$4\sqrt{15}+12-4\times 5-4\sqrt{5}\sqrt{3}$$

Multiply -4 and 5 to get -20.

$$4\sqrt{15}+12-20-4\sqrt{5}\sqrt{3}$$

Subtract 20 from 12 to get -8.

$$4\sqrt{15}-8-4\sqrt{5}\sqrt{3}$$

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

$$4\sqrt{15}-8-4\sqrt{15}$$

Combine 4\sqrt{15} and -4\sqrt{15} to get 0.

$$-8$$

Factor

$$-8$$