Factorize the expression completely:
[tex]27x^3-64[/tex]
Step 1: Applying exponent rule
[tex]\begin{gathered} 27x^3-64 \\ \mleft(3x\mright)^3-4^3 \end{gathered}[/tex]
Step 2: Applying difference of cubes formula
[tex]\begin{gathered} \mathrm{Apply\: Difference\: of\: Cubes\: Formula\colon\: }x^3-y^3=\mleft(x-y\mright)\mleft(x^2+xy+y^2\mright) \\ (3x)^3-4^3 \\ \mleft(3x\mright)^3-4^3=\mleft(3x-4\mright)\mleft(3^2x^2+4\cdot\: 3x+4^2\mright) \\ =\mleft(3x-4\mright)\mleft(3^2x^2+4\cdot\: 3x+4^2\mright) \\ =\mleft(3x-4\mright)\mleft(9x^2+12x+16\mright) \end{gathered}[/tex]
Therefore the correct answer is
[tex](3x-4)(9x^2+12x+16)[/tex]
