Solve 7(sqrt{2}+sqrt{3})(sqrt{2}-sqrt{3})

$$7 ( \sqrt { 2 } + \sqrt { 3 } ) ( \sqrt { 2 } - \sqrt { 3 } )$$

Evaluate

$$-7$$

Solution Steps

Use the distributive property to multiply 7 by \sqrt{2}+\sqrt{3}.

$$\left(7\sqrt{2}+7\sqrt{3}\right)\left(\sqrt{2}-\sqrt{3}\right)$$

Apply the distributive property by multiplying each term of 7\sqrt{2}+7\sqrt{3} by each term of \sqrt{2}-\sqrt{3}.

$$7\left(\sqrt{2}\right)^{2}-7\sqrt{3}\sqrt{2}+7\sqrt{3}\sqrt{2}-7\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{2} is 2.

$$7\times 2-7\sqrt{3}\sqrt{2}+7\sqrt{3}\sqrt{2}-7\left(\sqrt{3}\right)^{2}$$

Multiply 7 and 2 to get 14.

$$14-7\sqrt{3}\sqrt{2}+7\sqrt{3}\sqrt{2}-7\left(\sqrt{3}\right)^{2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$14-7\sqrt{6}+7\sqrt{3}\sqrt{2}-7\left(\sqrt{3}\right)^{2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$14-7\sqrt{6}+7\sqrt{6}-7\left(\sqrt{3}\right)^{2}$$

Combine -7\sqrt{6} and 7\sqrt{6} to get 0.

$$14-7\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$14-7\times 3$$

Multiply -7 and 3 to get -21.

$$14-21$$

Subtract 21 from 14 to get -7.

$$-7$$

Factor

$$-7$$