Solve (1+5sqrt{6})(1-5sqrt{6})

$$( 1 + 5 \sqrt { 6 } ) ( 1 - 5 \sqrt { 6 } )$$

Evaluate

$$-149$$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$1^{2}-\left(5\sqrt{6}\right)^{2}$$

Calculate 1 to the power of 2 and get 1.

$$1-\left(5\sqrt{6}\right)^{2}$$

Expand \left(5\sqrt{6}\right)^{2}.

$$1-5^{2}\left(\sqrt{6}\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$1-25\left(\sqrt{6}\right)^{2}$$

The square of \sqrt{6} is 6.

$$1-25\times 6$$

Multiply 25 and 6 to get 150.

$$1-150$$

Subtract 150 from 1 to get -149.

$$-149$$

Factor

$$-149$$