Question

X^4 - 1 =

Answer 1

Answer:

A

Step-by-step explanation:

Given

$x^{4}$ - 1 ← a difference of squares which factors in general as

a² - b² = (a - b)(a + b)

here $x^{4}$ = (x²)² ⇒ a = x² and b = 1

$x^{4}$ - 1 = (x² - 1)(x² + 1)

x² - 1 ← is a difference of squares and factors as

x² - 1 = (x - 1)(x + 1), so

(x² - 1)(x² + 1) = (x - 1)(x + 1)(x² + 1), hence

$x^{4}$ - 1 = (x - 1)(x + 1)(x² + 1) → A

Answer 2

Answer:

A.   (x + 1)(x - 1)(x^2 + 1).

Step-by-step explanation:

Using  the difference of 2 squares (a^2 - b^2 = (a + b)(a - b) :

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

Now repeating the difference of 2 squares on x^2 - 1:

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