Factor completely x^8-1

Question

Factor completely x^8-1

Answer 1

x⁸ - 1 = (x⁴ + 1)(x⁴ - 1) = (x⁴ + 1)(x² + 1)(x² - 1) = (x⁴ + 1)(x² + 1)(x + 1)(x - 1)

 

This is good practice with the difference of two squares.

 

Remember, a² - b² = (a + b)(a - b)

Answer 2

x⁸ - 1

(x⁴ + 1)(x⁴ - 1)

(x⁴ + 1)(x² + 1)(x² - 1)

(x⁴ + 1)(x² + 1)(x + 1)(x - 1)

 

This factoring over the set of real numbers.