Question

X^4 - 1

(x - 1) (x + 1) (x + i) (x - i)

(x - 1) (x - 1) (x - i) (x - i)

(x - 1) (x + i)

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

Answer 1

9514 1404 393

Answer:

(a) (x - 1) (x + 1) (x + i) (x - i)

Explanation:

Perhaps you want the fully factored form.

The difference of squares is factored as ...

a² -b² = (a -b)(a +b)

Your expression can be considered to be the difference of squares ...

(x²)² -(1)² = (x² -1)(x² +1)

Each of these factors can be considered to be the difference of squares:

x² -1 = (x -1)(x +1)

x² +1 = x² -(i²) = (x -i)(x +i)

So, the fully factored form is ...

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