[tex](x^2+\sqrt 2 x+1)^2[/tex]
[tex]=(x^2+\sqrt 2 x+1)(x^2+\sqrt 2 x+1)[/tex]
[tex]=x^2(x^2+\sqrt 2 x+1) + \sqrt{2} x (x^2+\sqrt 2 x+1) + 1(x^2+\sqrt 2 x+1)[/tex]
[tex]=x^4 + \sqrt{2} x^3 + x^2 + \sqrt{2}x^3 + 2x^2 + \sqrt{2}x + x^2+\sqrt 2 x+1[/tex]
[tex]=x^4 + 2\sqrt{2} x^3 + 4x^2 + 2 \sqrt{2}x +1[/tex]
That's the answer.
