Factor the sum or difference of two cubes.
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Question

Quizplus · Accepted Answer

The sum or difference of two cubes can be factored using the following formula:

a³ + b³ = (a + b)(a² – ab + b²)
a³ – b³ = (a – b)(a² + ab + b²)

In this case, the first term (a³) is 11ebb63d, and the second term (b³) is 1. Taking the cube root of each gives us a = 12d and b = 1. Plugging these values into the formula above, we get:

11ebb63d + 1 = (12d + 1)(144d² – 12d + 1)

Therefore, the answer is choice B. The given expression is not a perfect cube, but it can be factored as the difference of two cubes. Using the formula for the difference of two cubes, we have:
a^3 - b^3 = (a - b)(a^2 + ab + b^2)
In this case, a is x and b is 2. So we can write:
x^3 - 8 = (x - 2)(x^2 + 2x + 4)
Therefore, the answer is B.

Factor the Sum or Difference of Two Cubes