Question

Factor completely 16x^8 − 1.

Answer 1

Answer:

16x^8 − 1  = (4x^4 + 1)(2x^2 + 1)(2x^2 - 1)

Step-by-step explanation:

The difference of squares:

((ax)^2n - b) = (ax^n + b)(ax^n - b)

16x^8 − 1 = (4x^4 + 1)(4x^4 - 1)

(4x^4 - 1) = (2x^2 + 1)(2x^2 - 1)

16x^8 − 1  = (4x^4 + 1)(2x^2 + 1)(2x^2 - 1)