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The given expression is:

\[
9x^3 + 9x^2 - 64x - 64
\]

Let's break this down to completely factor the expression.

### Step 1: Grouping terms
We can group the terms in pairs to apply factoring by grouping:
\[
(9x^3 + 9x^2) - (64x + 64)
\]

### Step 2: Factor each group
Now, factor out the greatest common factor (GCF) from each group:

- In the first group, \(9x^2\) is common:
  \[
  9x^2(x + 1)
  \]

- In the second group, \(-64\) is common:
  \[
  -64(x + 1)
  \]

Now the expression becomes:
\[
9x^2(x + 1) - 64(x + 1)
\]

### Step 3: Factor out the common binomial
We can now factor out \((x + 1)\) from both terms:
\[
(x + 1)(9x^2 - 64)
\]

### Step 4: Factor the difference of squares
The term \(9x^2 - 64\) is a difference of squares, which can be factored as:
\[
9x^2 - 64 = (3x - 8)(3x + 8)
\]

### Final Factorization
Thus, the completely factored form of the expression is:
\[
(x + 1)(3x - 8)(3x + 8)
\]

Would you like further details or explanations on any step?

Here are 5 related questions:
1. How do you factor differences of squares in general?
2. What is the greatest common factor (GCF) and how is it used in factoring?
3. How would the factorization process change if the signs were different?
4. Can this method be used to factor higher degree polynomials?
5. How does grouping help in factoring polynomials with four terms?

**Tip:** When factoring polynomials, always look for common factors first. This simplifies the expression and makes factoring easier!

Completely factor the expression 9x^3 + 9x^2 - 64x - 64.

Explore the detailed steps to completely factor the cubic polynomial 9x^3 + 9x^2 - 64x - 64. This tutorial demonstrates the use of factoring by grouping and the difference of squares, suitable for high school students.

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