Solve (4sqrt{2}+3sqrt{5})(3sqrt{2}-4sqrt{5})

$$( 4 \sqrt { 2 } + 3 \sqrt { 5 } ) ( 3 \sqrt { 2 } - 4 \sqrt { 5 } )$$

Evaluate

$$-7\sqrt{10}-36\approx -58.135943621$$

Solution Steps

Apply the distributive property by multiplying each term of 4\sqrt{2}+3\sqrt{5} by each term of 3\sqrt{2}-4\sqrt{5}.

$$12\left(\sqrt{2}\right)^{2}-16\sqrt{2}\sqrt{5}+9\sqrt{5}\sqrt{2}-12\left(\sqrt{5}\right)^{2}$$

The square of \sqrt{2} is 2.

$$12\times 2-16\sqrt{2}\sqrt{5}+9\sqrt{5}\sqrt{2}-12\left(\sqrt{5}\right)^{2}$$

Multiply 12 and 2 to get 24.

$$24-16\sqrt{2}\sqrt{5}+9\sqrt{5}\sqrt{2}-12\left(\sqrt{5}\right)^{2}$$

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

$$24-16\sqrt{10}+9\sqrt{5}\sqrt{2}-12\left(\sqrt{5}\right)^{2}$$

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

$$24-16\sqrt{10}+9\sqrt{10}-12\left(\sqrt{5}\right)^{2}$$

Combine -16\sqrt{10} and 9\sqrt{10} to get -7\sqrt{10}.

$$24-7\sqrt{10}-12\left(\sqrt{5}\right)^{2}$$

The square of \sqrt{5} is 5.

$$24-7\sqrt{10}-12\times 5$$

Multiply -12 and 5 to get -60.

$$24-7\sqrt{10}-60$$

Subtract 60 from 24 to get -36.

$$-36-7\sqrt{10}$$