Answer:
C) (x – 2)(x + 2)(x² + 4)(x⁴ + 16)
Step-by-step explanation:
The difference of squares is factored like this:
... a² - b² = (a - b)(a + b)
The given expression is the difference of squares:
... (x⁴)² - (2⁴)²
so can be factored as ...
... (x⁴ - 2⁴)(x⁴ + 2⁴) . . . . . . . 2⁴=16
Once again, the difference term is the difference of squares, so it can be factored as ...
... x⁴ - 2⁴ = (x² -2²)(x² + 2²) . . . . . . 2²=4
And the difference in the first factor is also the difference of squares and can be factored.
... x² -2² = (x - 2)(x + 2)
Putting each factorization in its place in the whole expression, we get
... x⁸ - 256 = (x - 2)(x + 2)(x² +4)(x⁴ +16)
