Solve (1-sqrt{2})(1+sqrt{2})

$$(1- \sqrt{ 2 } )(1+ \sqrt{ 2 } )$$

Evaluate

$$-1$$

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}.

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

Calculate 1 to the power of 2 and get 1.

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

The square of \sqrt{2} is 2.

$$1-2$$

Subtract 2 from 1 to get -1.

$$-1$$

Factor

$$-1$$