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

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

Evaluate

$$2$$

Solution Steps

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

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

The square of \sqrt{2} is 2.

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

Add 2 and 1 to get 3.

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

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

$$3-2\sqrt{2}+2\sqrt{2}-2+1$$

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

$$3-2+1$$

Subtract 2 from 3 to get 1.

$$1+1$$

Add 1 and 1 to get 2.

$$2$$

Factor

$$2$$