Math Problem Statement

Simplify the polynomial expression: -7x^3 - x - 2y^3 + 3y^3 - x^3 + 3y^3 - 3x.

Solution

The given mathematical expression from the image is:

7x3x2y3+3y3x3+3y33x-7x^3 - x - 2y^3 + 3y^3 - x^3 + 3y^3 - 3x

Step-by-Step Simplification:

  1. Combine like terms involving x3x^3: 7x3x3=8x3-7x^3 - x^3 = -8x^3

  2. Combine like terms involving xx: x3x=4x-x - 3x = -4x

  3. Combine like terms involving y3y^3: 2y3+3y3+3y3=4y3-2y^3 + 3y^3 + 3y^3 = 4y^3

Final Simplified Expression:

8x3+4y34x-8x^3 + 4y^3 - 4x

Would you like further clarification or additional details?


Related Questions:

  1. What are "like terms" in algebra, and how are they identified?
  2. How does combining like terms simplify polynomial expressions?
  3. Can you provide examples of real-world problems where polynomials are used?
  4. What rules govern the addition and subtraction of terms with different variables or exponents?
  5. How can such expressions be visualized graphically?

Tip:

When simplifying expressions, group and combine terms with the same variable and exponent to avoid errors.