Answer
$(2x-3)(4x^2+6x+9)$
Work Step by Step
The student incorrectly used the factoring of the difference of $2$ squares. The factoring of the difference of $2$ cubes should instead be used.
The expressions $
8x^3
$ and $
27
$ are both perfect cubes (the cube root is exact). Hence, $
8x^3-27
$ is a $\text{
difference
}$ of $2$ cubes. Using the factoring of the sum or difference of $2$ cubes, which is given by $a^3+b^3=(a+b)(a^2-ab+b^2)$ or by $a^3-b^3=(a-b)(a^2+ab+b^2)$, the expression, $8x^3-27,$ is equivalent to
\begin{array}{l}\require{cancel}
(2x)^3-(3)^3
\\\\=
(2x-3)[(2x)^2+2x(3)+(3)^2]
\\\\=
(2x-3)(4x^2+6x+9)
.\end{array}
