Solve (sqrt{10}-sqrt{7})(-sqrt{10}-sqrt{7})

$$( \sqrt { 10 } - \sqrt { 7 } ) ( - \sqrt { 10 } - \sqrt { 7 } )$$

Evaluate

$$-3$$

Solution Steps

Apply the distributive property by multiplying each term of \sqrt{10}-\sqrt{7} by each term of -\sqrt{10}-\sqrt{7}.

$$\sqrt{10}\left(-\sqrt{10}\right)-\sqrt{10}\sqrt{7}-\sqrt{7}\left(-\sqrt{10}\right)+\left(\sqrt{7}\right)^{2}$$

To multiply \sqrt{10} and \sqrt{7}, multiply the numbers under the square root.

$$\sqrt{10}\left(-\sqrt{10}\right)-\sqrt{70}-\sqrt{7}\left(-\sqrt{10}\right)+\left(\sqrt{7}\right)^{2}$$

Multiply -1 and -1 to get 1.

$$\sqrt{10}\left(-\sqrt{10}\right)-\sqrt{70}+\sqrt{7}\sqrt{10}+\left(\sqrt{7}\right)^{2}$$

The square of \sqrt{7} is 7.

$$\sqrt{10}\left(-\sqrt{10}\right)-\sqrt{70}+\sqrt{7}\sqrt{10}+7$$

To multiply \sqrt{7} and \sqrt{10}, multiply the numbers under the square root.

$$\sqrt{10}\left(-\sqrt{10}\right)-\sqrt{70}+\sqrt{70}+7$$

Combine -\sqrt{70} and \sqrt{70} to get 0.

$$\sqrt{10}\left(-\sqrt{10}\right)+7$$

Multiply \sqrt{10} and \sqrt{10} to get 10.

$$10\left(-1\right)+7$$

Multiply 10 and -1 to get -10.

$$-10+7$$

Add -10 and 7 to get -3.

$$-3$$

Factor

$$-3$$