Solve 3sqrt{6}*(frac{(2-sqrt{6})(3sqrt{6}+9)}{-27}

$$3 \sqrt{ 6 } \times ( \frac{ (2- \sqrt{ 6 } )(3 \sqrt{ 6 } +9) }{ -27 }$$

Evaluate

$$2$$

Solution Steps

Apply the distributive property by multiplying each term of 2-\sqrt{6} by each term of 3\sqrt{6}+9.

$$3\sqrt{6}\times \frac{6\sqrt{6}+18-3\left(\sqrt{6}\right)^{2}-9\sqrt{6}}{-27}$$

The square of \sqrt{6} is 6.

$$3\sqrt{6}\times \frac{6\sqrt{6}+18-3\times 6-9\sqrt{6}}{-27}$$

Multiply -3 and 6 to get -18.

$$3\sqrt{6}\times \frac{6\sqrt{6}+18-18-9\sqrt{6}}{-27}$$

Subtract 18 from 18 to get 0.

$$3\sqrt{6}\times \frac{6\sqrt{6}-9\sqrt{6}}{-27}$$

Combine 6\sqrt{6} and -9\sqrt{6} to get -3\sqrt{6}.

$$3\sqrt{6}\times \frac{-3\sqrt{6}}{-27}$$

Divide -3\sqrt{6} by -27 to get \frac{1}{9}\sqrt{6}.

$$3\sqrt{6}\times \frac{1}{9}\sqrt{6}$$

Multiply 3 and \frac{1}{9} to get \frac{3}{9}.

$$\frac{3}{9}\sqrt{6}\sqrt{6}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{1}{3}\sqrt{6}\sqrt{6}$$

Multiply \sqrt{6} and \sqrt{6} to get 6.

$$\frac{1}{3}\times 6$$

Multiply \frac{1}{3} and 6 to get \frac{6}{3}.

$$\frac{6}{3}$$

Divide 6 by 3 to get 2.

$$2$$

Factor

$$2$$