Question

x to the power 8 minus 1

Answer 1

Answer:

(x - 1)(x + 1)(x² + 1)(x⁴ + 1)

Step-by-step explanation:

Given : x⁸ - 1

We can write this as :

→ (x⁴)² - (1)²

Identity : a² - b² = (a - b)(a + b)

Here, a = x⁴, b = 1

→ (x⁴ - 1)(x⁴ + 1)

We can write this as :

→ [ (x²)² - (1)² ] (x⁴ + 1)

Identity : a² - b² = (a - b)(a + b)

Here, a = x², b = 1

→ (x² - 1)(x² + 1)(x⁴ + 1)

We can write this as :

→ [ (x)² - (1)² ] (x² + 1)(x⁴ + 1)

Identity : a² - b² = (a - b)(a + b)

Here, a = x, b = 1

→ (x - 1)(x + 1)(x² + 1)(x⁴ + 1)