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

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

Evaluate

$$6$$

Solution Steps

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

$$-4\left(\sqrt{3}\right)^{2}-6\sqrt{3}\sqrt{2}+6\sqrt{3}\sqrt{2}+9\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{3} is 3.

$$-4\times 3-6\sqrt{3}\sqrt{2}+6\sqrt{3}\sqrt{2}+9\left(\sqrt{2}\right)^{2}$$

Multiply -4 and 3 to get -12.

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

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

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

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

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

Combine -6\sqrt{6} and 6\sqrt{6} to get 0.

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

The square of \sqrt{2} is 2.

$$-12+9\times 2$$

Multiply 9 and 2 to get 18.

$$-12+18$$

Add -12 and 18 to get 6.

$$6$$

Factor

$$2\times 3$$