The expression \( x^3 + 1 \) can be factored using the sum of cubes formula. The sum of cubes formula is:

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

For \( x^3 + 1 \):

- \( x = x \)
- \( y = 1 \) because \( 1 = 1^3 \)

Applying the formula:

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

Simplifying further:

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

So, the factored form of \( x^3 + 1 \) is:

\[
(x + 1)(x^2 - x + 1)
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you factor \( x^3 - 1 \)?
2. What is the difference between the sum of cubes and the difference of cubes?
3. How do you find the roots of the equation \( x^3 + 1 = 0 \)?
4. Can the sum of cubes be applied to higher powers like \( x^6 + 1 \)?
5. How would you factor \( 8x^3 + 1 \)?

**Tip:** When dealing with cubes, always identify if it's a sum or difference of cubes to apply the appropriate formula.

Learn how to factor the expression x^3 + 1 using the sum of cubes formula. This problem involves algebraic manipulation of polynomials and understanding the application of the sum of cubes formula to factorize cubic expressions. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation