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) + √(2) x (x^2+\sqrt 2 x+1) + 1(x^2+\sqrt 2 x+1)`

`=x^4 + √(2) x^3 + x^2 + √(2)x^3 + 2x^2 + √(2)x + x^2+\sqrt 2 x+1`

`=x^4 + 2√(2) x^3 + 4x^2 + 2 √(2)x +1`

That's the answer.