Solve 2{left(sqrt{2}-1right)}^2-2

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

Evaluate

$$4-4\sqrt{2}\approx -1.656854249$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\sqrt{2}-1\right)^{2}.

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

The square of \sqrt{2} is 2.

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

Add 2 and 1 to get 3.

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

Use the distributive property to multiply 2 by 3-2\sqrt{2}.

$$6-4\sqrt{2}-2$$

Subtract 2 from 6 to get 4.

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

Expand

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\sqrt{2}-1\right)^{2}.

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

The square of \sqrt{2} is 2.

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

Add 2 and 1 to get 3.

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

Use the distributive property to multiply 2 by 3-2\sqrt{2}.

$$6-4\sqrt{2}-2$$

Subtract 2 from 6 to get 4.

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