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

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

Evaluate

$$-6\sqrt{6}-6\approx -20.696938457$$

Solution Steps

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

$$9\left(\sqrt{2}\right)^{2}-12\sqrt{3}\sqrt{2}+6\sqrt{3}\sqrt{2}-8\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{2} is 2.

$$9\times 2-12\sqrt{3}\sqrt{2}+6\sqrt{3}\sqrt{2}-8\left(\sqrt{3}\right)^{2}$$

Multiply 9 and 2 to get 18.

$$18-12\sqrt{3}\sqrt{2}+6\sqrt{3}\sqrt{2}-8\left(\sqrt{3}\right)^{2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$18-12\sqrt{6}+6\sqrt{3}\sqrt{2}-8\left(\sqrt{3}\right)^{2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$18-12\sqrt{6}+6\sqrt{6}-8\left(\sqrt{3}\right)^{2}$$

Combine -12\sqrt{6} and 6\sqrt{6} to get -6\sqrt{6}.

$$18-6\sqrt{6}-8\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$18-6\sqrt{6}-8\times 3$$

Multiply -8 and 3 to get -24.

$$18-6\sqrt{6}-24$$

Subtract 24 from 18 to get -6.

$$-6-6\sqrt{6}$$

Factor

$$6 {(-\sqrt{6} - 1)} = -20.696938457$$