Answer
$(3x + 2)(9x^2 - 6x + 4)$
Work Step by Step
We see that $8 + 27x^3$ is the sum of two cubes.
Let's rewrite the expression so that the term of the greatest degree is first:
$27x^3 + 8$
We can factor the sum of two cubes using the following formula:
$(a + b)(a^2 - ab + b^2)$
We plug in the values, where $a = \sqrt[3] {27x^3}$ (or $a = 3x$) and $b = \sqrt[3] {8}$ (or $b = 2$:):
$(3x + 2)(9x^2 - (2)(3x) + 2^2)$
Let's simplify by multiplying the terms out:
$(3x + 2)(9x^2 - 6x + 4)$
