Math Problem Statement

Simplify the algebraic expression x^3 - y^3.

Solution

The image contains an expression written as x3y3x^3 - y^3.

This is a common algebraic expression that can be factored using the difference of cubes formula:

x3y3=(xy)(x2+xy+y2)x^3 - y^3 = (x - y)(x^2 + xy + y^2)

Would you like more details about this factoring process, or do you have any specific questions about it?

Here are 5 related questions for further exploration:

  1. How is the difference of cubes formula derived?
  2. What is the sum of cubes formula, and how does it differ from the difference of cubes?
  3. Can the expression x3y3x^3 - y^3 be solved for specific values of xx and yy?
  4. How does the difference of cubes formula apply to higher powers, like x6y6x^6 - y^6?
  5. What are the applications of factoring differences of cubes in real-world problems?

Tip: Whenever factoring a polynomial, look for common patterns like the difference of squares or cubes to simplify expressions.

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Math Problem Analysis

Mathematical Concepts

Algebra
Polynomial Factorization

Formulas

Difference of cubes formula: x^3 - y^3 = (x - y)(x^2 + xy + y^2)

Theorems

Difference of cubes

Suitable Grade Level

Grades 9-12