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

The Answer On Edge Is C.), Have Fun Dreamers!

Explanation:

Answer 2

C) (x – 2)(x + 2)(x² + 4)(x⁴ + 16)

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)