The expression \( a^3 + 125 \) can be factored using the sum of cubes formula. The sum of cubes formula is:

\[
x^3 + y^3 = (x + y)(x^2 - xy + y^2)
\]

In your case:

- \( x = a \)
- \( y = 5 \) because \( 125 = 5^3 \)

Applying the formula:

\[
a^3 + 125 = a^3 + 5^3 = (a + 5)(a^2 - 5a + 25)
\]

So, the factored form of \( a^3 + 125 \) is:

\[
(a + 5)(a^2 - 5a + 25)
\]

Would you like more details or have any questions about this? 

Here are 5 related questions:
1. How do you factor a difference of cubes?
2. What is the general formula for the sum of cubes?
3. How can you verify the factorization of a cubic expression?
4. What are some real-world applications of the sum of cubes?
5. How would you factor \( a^3 - 125 \)?

**Tip:** Always check your factorization by expanding it back to the original expression to ensure it's correct.

Learn how to factor the expression a^3 + 125 using the sum of cubes formula. This problem involves algebraic manipulation and the application of the sum of cubes formula to factor cubic expressions. Suitable for students in Grades 9-12.

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