Question

What is the product of (x^2+√2x+1)(x^2+√2x+1)

Answer 1

$(x^2+\sqrt 2 x+1)^2$

$=(x^2+\sqrt 2 x+1)(x^2+\sqrt 2 x+1)$

$=x^2(x^2+\sqrt 2 x+1) + \sqrt{2} x (x^2+\sqrt 2 x+1) + 1(x^2+\sqrt 2 x+1)$

$=x^4 + \sqrt{2} x^3 + x^2 + \sqrt{2}x^3 + 2x^2 + \sqrt{2}x + x^2+\sqrt 2 x+1$

$=x^4 + 2\sqrt{2} x^3 + 4x^2 + 2 \sqrt{2}x +1$

That's the answer.