Polynomial question

(x+[1+√2]) (x-[1-√2])  =

x^2 + x(1+√2) - x(1-√2) - (1+√2)(1-√2) =

x^2 + x + √(2)x - x + √(2)x - ( 1 - 2) =

x^2 + 2√(2)x + 1

Sorry it is too difficult to display  on my phone.

but

just expand it like a normal quadratic.

(x+[1+√2])(x-[1-√2])

$$\\ \small{\text{
$
(x+[1+\sqrt{2}])(x-[1-\sqrt{2}]) = [ ( x+\sqrt{2} ) +1] [(x+\sqrt{2})-1]=( x+\sqrt{2} )^2-1= x^2-2\sqrt{2}x+2-1
$
}}$\\$
\small{\text{
$=x^2-2\sqrt{2}x+1
$
}}$$