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

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

Evaluate

$$2\left(2\sqrt{10}+5\sqrt{5}-10\sqrt{2}-8\right)\approx -9.274480832$$

Solution Steps

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

$$4\sqrt{5}\sqrt{2}+10\sqrt{5}-8\left(\sqrt{2}\right)^{2}-20\sqrt{2}$$

To multiply \sqrt{5} and \sqrt{2}, multiply the numbers under the square root.

$$4\sqrt{10}+10\sqrt{5}-8\left(\sqrt{2}\right)^{2}-20\sqrt{2}$$

The square of \sqrt{2} is 2.

$$4\sqrt{10}+10\sqrt{5}-8\times 2-20\sqrt{2}$$

Multiply -8 and 2 to get -16.

$$4\sqrt{10}+10\sqrt{5}-16-20\sqrt{2}$$

Factor

$$2 {(2 \sqrt{10} + 5 \sqrt{5} - 10 \sqrt{2} - 8)} = -9.274480832$$