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

Answer:AStep-by-step explanation:Given[tex]x^{4}[/tex] - 1 ← a difference of squares which factors in general asa² - b² = (a - b)(a + b)here [tex]x^{4}[/tex] = (x²)² ⇒ a = x² and b = 1[tex]x^{4}[/tex] - 1 = (x² - 1)(x² + 1)x² - 1 ← is a difference of squares and factors asx² - 1 = (x - 1)(x + 1), so(x² - 1)(x² + 1) = (x - 1)(x + 1)(x² + 1), hence[tex]x^{4}[/tex] - 1 = (x - 1)(x + 1)(x² + 1) → A