Solve (sqrt{7}+2sqrt{5})(sqrt{7}-4sqrt{5})=

$$( \sqrt { 7 } + 2 \sqrt { 5 } ) ( \sqrt { 7 } - 4 \sqrt { 5 } ) =$$

Evaluate

$$-2\sqrt{35}-33\approx -44.832159566$$

Solution Steps

Apply the distributive property by multiplying each term of \sqrt{7}+2\sqrt{5} by each term of \sqrt{7}-4\sqrt{5}.

$$\left(\sqrt{7}\right)^{2}-4\sqrt{7}\sqrt{5}+2\sqrt{5}\sqrt{7}-8\left(\sqrt{5}\right)^{2}$$

The square of \sqrt{7} is 7.

$$7-4\sqrt{7}\sqrt{5}+2\sqrt{5}\sqrt{7}-8\left(\sqrt{5}\right)^{2}$$

To multiply \sqrt{7} and \sqrt{5}, multiply the numbers under the square root.

$$7-4\sqrt{35}+2\sqrt{5}\sqrt{7}-8\left(\sqrt{5}\right)^{2}$$

To multiply \sqrt{5} and \sqrt{7}, multiply the numbers under the square root.

$$7-4\sqrt{35}+2\sqrt{35}-8\left(\sqrt{5}\right)^{2}$$

Combine -4\sqrt{35} and 2\sqrt{35} to get -2\sqrt{35}.

$$7-2\sqrt{35}-8\left(\sqrt{5}\right)^{2}$$

The square of \sqrt{5} is 5.

$$7-2\sqrt{35}-8\times 5$$

Multiply -8 and 5 to get -40.

$$7-2\sqrt{35}-40$$

Subtract 40 from 7 to get -33.

$$-33-2\sqrt{35}$$