MATH SOLVE

9 months ago

Q:
# 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)

Accepted Solution

A:

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)²so can be factored as ...... (x⁴ - 2⁴)(x⁴ + 2⁴) . . . . . . . 2⁴=16Once again, the difference term is the difference of squares, so it can be factored as ...... x⁴ - 2⁴ = (x² -2²)(x² + 2²) . . . . . . 2²=4And 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)