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The expression given is \( 8 + m^3 \). This is a sum of cubes, as \( 8 = 2^3 \). We can factor a sum of cubes using the following formula:

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

In this case:
- \( a = 2 \)
- \( b = m \)

Now applying the sum of cubes formula:

\[
8 + m^3 = (2 + m)(2^2 - 2m + m^2)
\]

Simplifying the expression inside the second parentheses:

\[
8 + m^3 = (2 + m)(4 - 2m + m^2)
\]

Thus, the fully factored form of \( 8 + m^3 \) is:

\[
(2 + m)(4 - 2m + m^2)
\]

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

Here are 5 related questions:
1. How do you factor differences of cubes, such as \( a^3 - b^3 \)?
2. Can you factor a sum of higher powers, like \( a^4 + b^4 \)?
3. How can you verify if your factorization is correct?
4. What is the significance of factoring polynomials in solving equations?
5. How does factoring help in simplifying expressions?

**Tip:** Always check if the expression is a special case (like sum/difference of cubes or squares) to simplify factoring!

Learn how to factor the polynomial 8 + m^3 completely using the sum of cubes formula: (a + b)(a^2 - ab + b^2). This problem is suitable for students in Grades 9-11 and covers important algebraic concepts in polynomial factoring.

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