multiply (1-x+x2)(1-x+x2)?

(1-x+x²)(1-x+x²) =

(x^4 - x^3 + x^2) + (-x^3 + x^2 - x) + (x^2 - x + 1) =

x^4 - 2x^3 + 3x² - 2x + 1

1 - x + x²
_- x + x² - x³
_____x² - x³ + x^4

1 - 2x + 3x² - 2x³ + x^4

1-2x+3x2-2x3+x4

(1 - x + x^2)(1 - x + x^2)
= (x^2 - x + 1)(x^2 - x + 1)
= x^4 - x^3 + x^2 - x^3 + x^2 - x + x^2 - x + 1
= x^4 - x^3 - x^3 + x^2 + x^2 + x^2 - x - x + 1
= x^4 - 2x^3 + 3x^2 - 2x + 1

1 - x + x^2 - x + x^2 - x^3 + x^2 - x^3 + x^4

= x^4 - 2x^3 + 3x^2 - 2x + 1

If x2 is x*2 (multiplied), then (x-x2-1)^2

If x2 is x^2 (squared), then (x^2-x+1)^2

1-x+x²)(1-x+x²) =

(x^4 - x^3 + x^2) + (-x^3 + x^2 - x) + (x^2 - x + 1) =

x^4 - 2x^3 + 3x² - 2x + 1

(1-x+x²)(1-x+x²)=1(1-x+x²)-x(1-x+x²)+x²(1-x+x²)
=1-x+x²-x+x²-x^3+x²-x^3+x^4
Regrouping the terms we get it as x^4-2x^3+3x²-2x+1

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

(1-x+x^2)+(-x+x^2+x^3)+(x^2+-x^3+x^4)
^^^Distributed each number and multiplied it to
the second number. I.E. 1x1, -x*-x

2x^4+x^3+3x^2+(x+-x)+1
^^Added common terms^^

x^4+2x^3+3x^2+1

1-x+x^2-x+x^2-x^3+x^2-x^3+x^4
= x^4-2x^3+3x^2-2x+1