Solve (8-9sqrt{6})(9+2sqrt{6})

$$(8-9 \sqrt{ 6 } )(9+2 \sqrt{ 6 } )$$

Evaluate

$$-65\sqrt{6}-36\approx -195.216833281$$

Solution Steps

Apply the distributive property by multiplying each term of 8-9\sqrt{6} by each term of 9+2\sqrt{6}.

$$72+16\sqrt{6}-81\sqrt{6}-18\left(\sqrt{6}\right)^{2}$$

Combine 16\sqrt{6} and -81\sqrt{6} to get -65\sqrt{6}.

$$72-65\sqrt{6}-18\left(\sqrt{6}\right)^{2}$$

The square of \sqrt{6} is 6.

$$72-65\sqrt{6}-18\times 6$$

Multiply -18 and 6 to get -108.

$$72-65\sqrt{6}-108$$

Subtract 108 from 72 to get -36.

$$-36-65\sqrt{6}$$