Question

Which expression is equivalent to x8 - 256?

A) (x – 2)(x + 2)(x2 + 8)(x4 + 8)
B) (x – 2)(x – 2)(x2 + 4)(x4 + 16)
C) (x – 2)(x + 2)(x2 + 4)(x4 + 16)
D) (x + 2)(x + 2)(x2 + 4)(x4 + 16)

Answer 1

we have that
case A)
(x – 2)(x + 2)(x² + 8)(x4 + 8)
(x²-4)(x² + 8)(x4 + 8)

case B)
(x – 2)(x – 2)(x² + 4)(x4 + 16)
(x-2)²(x² + 4)(x4 + 16)

case C)
(x – 2)(x + 2)(x² + 4)(x4 + 16)
(x²-4)(x² + 4)(x4 + 16)
(x4 -16)(x4 + 16)
(x8-256)

case D)
(x + 2)(x + 2)(x² + 4)(x4 + 16)
(x+2)²(x² + 4)(x4 + 16)

the answer is
the option
C) (x – 2)(x + 2)(x2 + 4)(x4 + 16)