How can i simplify x^4 -2x^2 +1 ?

x^4 - 2x^2 + 1
= x^4 - x^2 - x^2 + 1
= (x^4 - x^2) - (x^2 - 1)
= x^2(x^2 - 1) - 1(x^2 - 1)
= (x^2 - 1)(x^2 - 1)
= (x^2 + x - x - 1)(x^2 + x - x - 1)
= [(x^2 + x) - (x + 1)][(x^2 + x) - (x + 1)]
= [x(x + 1) - 1(x + 1)][x(x + 1) - 1(x + 1]
= (x + 1)(x - 1)(x + 1)(x - 1)
= (x + 1)(x + 1)(x - 1)(x - 1)
= [(x + 1)(x - 1)]^2

(x-1)^2 (x+1)^2
use synthetic division to divide X^4-2x^2+1 and use either 1 or -1 and keep going til everything is simplified i think

x^4 -2x^2 +1 = (x^2-1)^2
= (x^2-1) (x^2-1)
= (x-1)(x+1)(x-1)(x+1)

It is already simplified. If you want to factor it:

x^4 - 2x² + 1
= (x²)² - 2×x²×1 + 1²
= (x²-1)²
= (x²-1²)²
= [(x+1)(x-1)]²
= (x+1)²(x-1)²

how the 1st one i've got been given a million. in case you ingredient out all the expressions you will possibly see that all of them tournament those interior the denominator so as that all of them cancel out. for the 2d i uncertain, yet i've got been given 2/x-y. i placed all the variables with adverse powers and placed them in a denominator then i simplified and ended up with a million/.5x-.5y , so i in basic terms mulptipy the entire issue by skill of two to make the backside an entire huge style

(x ² - 1)(x² - 1)
(x - 1)(x + 1)(x - 1)(x + 1)
(x - 1) ² (x + 1) ²

this is quadraric is x^2

so x^4- 2x^2 + 1= (x^2-1)^2

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

so x^4- 2x^2 + 1= (x^2-1)^2 = (x+1)^2(x-1)^2

HINT:
It might look like a quartic... but its really the quadratic of quadratics.