Math Problem Statement

ans

Simplify the expression: ((a + b)^3 + (b + c)^3 + (c + a)^3 - 3(a + b)(b + c)(c + a)) / (a^3 + b^3 + c^3 - 3abc)

Solution

The given expression simplifies to 22. Thus, the correct answer is:

(B) 2

Would you like a detailed explanation, or do you have any questions?

Here are 5 related questions to explore:

  1. How do you expand binomial expressions like (a+b)3(a + b)^3?
  2. What are some general simplification techniques for cubic polynomials?
  3. How does factorization help in simplifying algebraic expressions?
  4. What is the role of symmetry in expressions involving multiple variables like aa, bb, and cc?
  5. Can this simplification method be applied to other types of algebraic fractions?

Tip: When simplifying algebraic fractions, always look for common patterns like binomial expansions or factorizations!

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Math Problem Analysis

Mathematical Concepts

Algebra
Polynomial Expansion
Simplification
Cubic Expressions

Formulas

Binomial expansion: (x + y)^3 = x^3 + 3x^2y + 3xy^2 + y^3
Factorization: a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca)

Theorems

Binomial Theorem
Factorization of symmetric polynomials

Suitable Grade Level

Grades 9-12