Solve (4+sqrt{6})(2-8sqrt{6})

$$( 4 + \sqrt { 6 } ) ( 2 - 8 \sqrt { 6 } )$$

Evaluate

$$-30\sqrt{6}-40\approx -113.484692283$$

Solution Steps

Apply the distributive property by multiplying each term of 4+\sqrt{6} by each term of 2-8\sqrt{6}.

$$8-32\sqrt{6}+2\sqrt{6}-8\left(\sqrt{6}\right)^{2}$$

Combine -32\sqrt{6} and 2\sqrt{6} to get -30\sqrt{6}.

$$8-30\sqrt{6}-8\left(\sqrt{6}\right)^{2}$$

The square of \sqrt{6} is 6.

$$8-30\sqrt{6}-8\times 6$$

Multiply -8 and 6 to get -48.

$$8-30\sqrt{6}-48$$

Subtract 48 from 8 to get -40.

$$-40-30\sqrt{6}$$

Factor

$$10 {(-3 \sqrt{6} - 4)} = -113.484692283$$