X^4 - 1 =
a. (x+1)(x-1)(x^2+1)
b. ( x+1)^2(x-1)^2
c. (x+1)^3(x-1)^1
d. (x-1)^4

A

Step-by-step explanation:

Given

- 1 ← a difference of squares which factors in general as

a² - b² = (a - b)(a + b)

here = (x²)² ⇒ a = x² and b = 1

- 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

- 1 = (x - 1)(x + 1)(x² + 1) → A

(5x-1)^2= (5x)^2-2(5x)×1+(1)^2=25x^2-10x+1

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