Solve -(sqrt{2}+sqrt{3})(sqrt{3}-sqrt{2})

$$- ( \sqrt { 2 } + \sqrt { 3 } ) ( \sqrt { 3 } - \sqrt { 2 } )$$

Evaluate

$$-1$$

Solution Steps

To find the opposite of \sqrt{2}+\sqrt{3}, find the opposite of each term.

$$\left(-\sqrt{2}-\sqrt{3}\right)\left(\sqrt{3}-\sqrt{2}\right)$$

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

$$\left(-\sqrt{2}\right)^{2}-\left(\sqrt{3}\right)^{2}$$

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

$$\left(-1\right)^{2}\left(\sqrt{2}\right)^{2}-\left(\sqrt{3}\right)^{2}$$

Calculate -1 to the power of 2 and get 1.

$$1\left(\sqrt{2}\right)^{2}-\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{2} is 2.

$$1\times 2-\left(\sqrt{3}\right)^{2}$$

Multiply 1 and 2 to get 2.

$$2-\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$2-3$$

Subtract 3 from 2 to get -1.

$$-1$$

Factor

$$-1$$