Question

What is the factored form of n³ + 512?

A. (n - 8) (n² + 8n+64)
B. (n + 4)(n² - 4n + 128)
C. (n - 4)(n² + 4n + 128)
D. (n + 8)(n² - 8n + 64)

Answer 1

The factored form of n³ + 512 is (n + 8)(n² - 8n + 64), which corresponds to option D.

Step-by-step explanation:

The factored form of n³ + 512 is (n + 8)(n² - 8n + 64), which corresponds to option D.

To factorize the given expression, we can use the sum of cubes formula:

a³ + b³ = (a + b)(a² - ab + b²).

In this case, a = n and b = 8.

Plugging in these values, we get:

n³ + 512 = (n + 8)(n² - 8n + 64).

Therefore, option D is the correct factored form of the expression.