To simplify the expression \( 6p^3 + 6 \), we can factor out the common factor between the two terms. 

### Step 1: Factor out the Greatest Common Factor (GCF)
The GCF of \( 6p^3 \) and \( 6 \) is \( 6 \).

### Step 2: Factor the expression
\[
6p^3 + 6 = 6(p^3 + 1)
\]

### Step 3: Check if further factoring is possible
The expression inside the parentheses is \( p^3 + 1 \), which is a sum of cubes. The sum of cubes can be factored using the formula:

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

Here, \( p^3 + 1 \) can be rewritten as:

\[
p^3 + 1^3 = (p + 1)(p^2 - p \cdot 1 + 1^2)
\]

Simplifying further:

\[
p^3 + 1 = (p + 1)(p^2 - p + 1)
\]

### Final Factored Form
\[
6p^3 + 6 = 6(p + 1)(p^2 - p + 1)
\]

Would you like more details or have any questions?

### Related Questions:
1. How do you factor other types of polynomial expressions, such as differences of cubes?
2. What are the steps to identify the Greatest Common Factor in polynomials?
3. How can we apply the factoring of sums and differences of cubes in solving equations?
4. What are some real-world applications of factoring polynomials?
5. How do you factor expressions that include higher powers or multiple terms?

### Tip:
When factoring sums of cubes, always check if there is a GCF to factor out first before applying special formulas.

Explore how to factor the polynomial expression 6p^3 + 6 by first factoring out the greatest common factor (GCF) and then applying the sum of cubes formula. This step-by-step guide is ideal for students in Grades 9-10 looking to strengthen their algebra skills.

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