The expression you've given is \( 6p^3 + 6 \).

This expression cannot be simplified further, but you can factor out the common factor:

\[
6p^3 + 6 = 6(p^3 + 1)
\]

Now, the expression \( p^3 + 1 \) can be factored further using the sum of cubes formula \( a^3 + b^3 = (a + b)(a^2 - ab + b^2) \). Here, \( p^3 + 1 \) can be rewritten as:

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

Therefore, the fully factored form of the expression is:

\[
6(p + 1)(p^2 - p + 1)
\]

Would you like more details on the factoring process or have any other questions?

Here are some related questions:
1. What is the difference between factoring and simplifying an expression?
2. How do you apply the sum of cubes formula?
3. What other forms can the expression \( p^3 + 1 \) take?
4. How do you factor expressions with different degrees?
5. What is the significance of recognizing common factors in an expression?

**Tip:** When factoring polynomials, always look for common factors first before applying more complex factorization techniques.

Explore the detailed process of factoring the polynomial 6p^3 + 6 by first factoring out the common factor and then applying the sum of cubes formula. This problem is ideal for students in Grades 9-12 and covers key algebraic concepts such as polynomials and factoring techniques.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation