Question

8x^3 -1
(2x)^3 - 1^3
(2x-1)(2x^2 + 2x + 1^2) -> but this doesnt factor

Answer 1

Since a^3 - b^3 = (a-b)(a^2 + ab + b^2)
Substitute a = 2x and b = 1
8x^3 -1 = (2x - 1)(4x^2 + 2x + 1)
You are right that the second term cannot be factored into monomials with real coefficients.

Answer 2

Thats what I thought but I was not sure. Thanks so much.