The given expression is
[tex]8x^3-27[/tex]To find the equivalent expression, we use the formula for the difference of perfect cubes.
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]But, we have to express the numbers 8 and 27 as cubic powers.
[tex]\begin{gathered} 8=2\cdot2\cdot2=2^3 \\ 27=3\cdot3\cdot3=3^3 \end{gathered}[/tex]Then, we know that a and b are
[tex]\begin{gathered} a=2x \\ b=3 \end{gathered}[/tex]So, the difference would be
[tex](2x)^3-(3)^3[/tex]Once we have the difference expressed in cubes, we apply the formula using the a and b values we determined before.
[tex](2x)^3-(3)^3=(2x-3)((2x)^2+(2x)(3)+(3)^2)_{}=(2x-3)(4x^2_{}+6x+9)[/tex]Therefore, the factors are
[tex](2x-3)(4x^2+6x+9)_{}[/tex]