The expression \(64x^3 - 27y^3\) is a difference of cubes. It can be factored using the difference of cubes formula:

\[
a^3 - b^3 = (a - b)(a^2 + ab + b^2)
\]

In this case, \(a = 4x\) and \(b = 3y\).

Let's apply the formula:

\[
64x^3 - 27y^3 = (4x)^3 - (3y)^3 = (4x - 3y)((4x)^2 + (4x)(3y) + (3y)^2)
\]

Now, let's simplify the terms inside the second factor:

\[
(4x - 3y)(16x^2 + 12xy + 9y^2)
\]

So, the factored form of \(64x^3 - 27y^3\) is:

\[
64x^3 - 27y^3 = (4x - 3y)(16x^2 + 12xy + 9y^2)
\]

Would you like more details or have any questions?

Here are 5 questions you might be interested in:
1. How do you factor a sum of cubes?
2. What is the quadratic formula and how is it used?
3. Can you explain how to solve polynomial equations?
4. What are the properties of exponents?
5. How do you find the roots of a cubic equation?

Tip: When factoring expressions, always check if the expression fits a common factorization formula, such as the difference of squares or the difference of cubes, to simplify your work.

Learn how to factor the expression 64x^3 - 27y^3 using the difference of cubes formula. This problem involves polynomial algebra and covers key concepts such as factoring and polynomial identities. Suitable for students in Grades 9-12.

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