Factor x^8-1

Problem

x8−1

Solution

1. Identify the expression as a difference of squares, which follows the pattern a2−b2=(a−b)*(a+b)

2. Apply the formula to the initial expression by treating x8 as (x4)2 and 1 as 1

x8−1=(x4−1)*(x4+1)

3. Factor the resulting term (x4−1) as another difference of squares.

(x4−1)*(x4+1)=(x2−1)*(x2+1)*(x4+1)

4. Factor the term (x2−1) as a difference of squares one last time.

(x2−1)*(x2+1)*(x4+1)=(x−1)*(x+1)*(x2+1)*(x4+1)

Final Answer

x8−1=(x−1)*(x+1)*(x2+1)*(x4+1)

Want more problems? Check here!