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

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

Evaluate

$$3$$

Solution Steps

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

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

The square of \sqrt{2} is 2.

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

Add 2 and 1 to get 3.

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

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

$$3$$

Factor

$$3$$