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 . 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:
- How do you expand binomial expressions like ?
- What are some general simplification techniques for cubic polynomials?
- How does factorization help in simplifying algebraic expressions?
- What is the role of symmetry in expressions involving multiple variables like , , and ?
- 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