Solve (3sqrt{2}-6sqrt{5})(5sqrt{2}+10sqrt{5})

$$( 3 \sqrt { 2 } - 6 \sqrt { 5 } ) ( 5 \sqrt { 2 } + 10 \sqrt { 5 } )$$

Evaluate

$$-270$$

Solution Steps

Apply the distributive property by multiplying each term of 3\sqrt{2}-6\sqrt{5} by each term of 5\sqrt{2}+10\sqrt{5}.

$$15\left(\sqrt{2}\right)^{2}+30\sqrt{2}\sqrt{5}-30\sqrt{5}\sqrt{2}-60\left(\sqrt{5}\right)^{2}$$

The square of \sqrt{2} is 2.

$$15\times 2+30\sqrt{2}\sqrt{5}-30\sqrt{5}\sqrt{2}-60\left(\sqrt{5}\right)^{2}$$

Multiply 15 and 2 to get 30.

$$30+30\sqrt{2}\sqrt{5}-30\sqrt{5}\sqrt{2}-60\left(\sqrt{5}\right)^{2}$$

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

$$30+30\sqrt{10}-30\sqrt{5}\sqrt{2}-60\left(\sqrt{5}\right)^{2}$$

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

$$30+30\sqrt{10}-30\sqrt{10}-60\left(\sqrt{5}\right)^{2}$$

Combine 30\sqrt{10} and -30\sqrt{10} to get 0.

$$30-60\left(\sqrt{5}\right)^{2}$$

The square of \sqrt{5} is 5.

$$30-60\times 5$$

Multiply -60 and 5 to get -300.

$$30-300$$

Subtract 300 from 30 to get -270.

$$-270$$

Factor

$$-270$$