The given expression is \( x^3 + 125 \). This is a sum of cubes, since \( 125 = 5^3 \). The sum of cubes can be factored using the following identity:

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

In this case, \( a = x \) and \( b = 5 \), so we can rewrite the expression as:

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

Thus, the factored form of \( x^3 + 125 \) is:

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

Would you like any further explanation or details?

Here are 5 related questions for deeper understanding:

1. How can we factor the difference of cubes?
2. What are some real-life applications of factoring cubic expressions?
3. Can the quadratic factor \( x^2 - 5x + 25 \) be factored further?
4. How do you find the roots of a cubic equation?
5. What is the graphical representation of \( x^3 + 125 \)?

**Tip**: For cubic equations, always check if the sum or difference of cubes formula applies to simplify them easily.

Learn how to factor the cubic expression x³ + 125 using the sum of cubes formula. This algebra problem is ideal for high school students in Grades 9-12, focusing on factoring and the sum of cubes theorem.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation