You have the expression $64x^3 - 27$.

This can be factored as a difference of cubes, since $64x^3$ is the cube of $4x$, and $27$ is the cube of $3$.

The difference of cubes formula is:

$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$

In this case:

• $a = 4x$
• $b = 3$

Using the formula:

$64x^3 - 27 = (4x - 3)((4x)^2 + (4x)(3) + (3)^2)$

Simplifying further:

$64x^3 - 27 = (4x - 3)(16x^2 + 12x + 9)$

Thus, the factored form is:

$64x^3 - 27 = (4x - 3)(16x^2 + 12x + 9)$

Would you like any additional details or further explanation?

Here are some related questions you might find helpful:

1. How can I factor the sum of cubes, similar to the difference of cubes?
2. Can you explain the steps for factoring trinomials?
3. What is the general process for factoring polynomials of higher degrees?
4. How does factoring help in solving polynomial equations?
5. What are some common factorization formulas used in algebra?

Tip: Always check if a polynomial can be factored using special formulas like the difference or sum of cubes to simplify your work.