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

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

Evaluate

$$2$$

Solution Steps

Use the distributive property to multiply 2 by \sqrt{2}-1.

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

Apply the distributive property by multiplying each term of 2\sqrt{2}-2 by each term of \sqrt{2}+1.

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

The square of \sqrt{2} is 2.

$$2\times 2+2\sqrt{2}-2\sqrt{2}-2$$

Multiply 2 and 2 to get 4.

$$4+2\sqrt{2}-2\sqrt{2}-2$$

Combine 2\sqrt{2} and -2\sqrt{2} to get 0.

$$4-2$$

Subtract 2 from 4 to get 2.

$$2$$

Factor

$$2$$