Odpowiedź:
[tex]\left(\sqrt{2}+1\right)^2=\left(\sqrt{2}\right)^2+2\sqrt{2}\cdot \:1+1^2=3+2\sqrt{2}[/tex]
[tex]\left(\sqrt{2}-1\right)^2=\left(\sqrt{2}\right)^2-2\sqrt{2}\cdot \:1+1^2=3-2\sqrt{2}[/tex]
[tex]\left(\sqrt{2}+1\right)^2-\left(\sqrt{2}-1\right)^2=3+2\sqrt{2}-\left(3-2\sqrt{2}\right)=3+2\sqrt{2}-3+2\sqrt{2}=2\sqrt{2}+2\sqrt{2}=\boxed{4\sqrt{2}}[/tex]