Factor completely x^8-16

A.) (x^4 - 4) (x^4 + 4)

B.) (x^2 - 2) (x^2 + 2) (x^4+4)

C.) (x^2 - 2) (x^2 + 2) (x^4-4)

D.) (x^2-2) (x^2-2) (x^4-4)

B.) (x^2 - 2) (x^2 + 2) (x^4+4)

Step-by-step explanation:

x⁸ - 16

(x⁴) ² - 4²

(x⁴ - 4) (x⁴ + 4)

[ (x²) ² - 2²] (x⁴ + 4)

(x² - 2) (x² + 2) (x⁴ + 4)

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

Step-by-step explanation:

x^8-16

We know this is the difference of squares a^2 - b^2 = (a-b) (a+b)

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

We also recognize the x^4 - 4 is the difference of squares

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

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