Question

(x-1) (x+1) (x2+1) (x4+1)​

Answer 1

Answer :

x⁸ - 1

Step-by-step explanation :

(x - 1)(x + 1)(x² + 1)(x⁴ + 1)

Identity Used : (a - b)(a + b) = a² - b²

→ [ (x - 1)(x + 1) ] (x² + 1)(x⁴ + 1)

Here, a = x, b = 1

→ [ (x)² - (1)² ] (x² + 1)(x⁴ + 1)

→ (x² - 1)(x² + 1)(x⁴ + 1)

→ [ (x² - 1)(x² + 1) ] (x⁴ + 1)

Here, a = x², b = 1

→ [ (x²)² - (1)² ] (x⁴ + 1)

→ (x⁴ - 1)(x⁴ + 1)

Here, a = x⁴, b = 1

→ (x⁴)² - (1)²

→ x⁸ - 1