Solve (7sqrt{10}+3sqrt{7})(sqrt{10}-9sqrt{7})

$$( 7 \sqrt { 10 } + 3 \sqrt { 7 } ) ( \sqrt { 10 } - 9 \sqrt { 7 } )$$

Evaluate

$$-60\sqrt{70}-119\approx -620.99601592$$

Solution Steps

Apply the distributive property by multiplying each term of 7\sqrt{10}+3\sqrt{7} by each term of \sqrt{10}-9\sqrt{7}.

$$7\left(\sqrt{10}\right)^{2}-63\sqrt{10}\sqrt{7}+3\sqrt{7}\sqrt{10}-27\left(\sqrt{7}\right)^{2}$$

The square of \sqrt{10} is 10.

$$7\times 10-63\sqrt{10}\sqrt{7}+3\sqrt{7}\sqrt{10}-27\left(\sqrt{7}\right)^{2}$$

Multiply 7 and 10 to get 70.

$$70-63\sqrt{10}\sqrt{7}+3\sqrt{7}\sqrt{10}-27\left(\sqrt{7}\right)^{2}$$

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

$$70-63\sqrt{70}+3\sqrt{7}\sqrt{10}-27\left(\sqrt{7}\right)^{2}$$

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

$$70-63\sqrt{70}+3\sqrt{70}-27\left(\sqrt{7}\right)^{2}$$

Combine -63\sqrt{70} and 3\sqrt{70} to get -60\sqrt{70}.

$$70-60\sqrt{70}-27\left(\sqrt{7}\right)^{2}$$

The square of \sqrt{7} is 7.

$$70-60\sqrt{70}-27\times 7$$

Multiply -27 and 7 to get -189.

$$70-60\sqrt{70}-189$$

Subtract 189 from 70 to get -119.

$$-119-60\sqrt{70}$$

Factor

$$-60\sqrt{70}-119$$