Math Problem Statement

Which of the following expressions is equivalent to: (4x^3 - 5x) + (8x - 3x^3)?

Solution

We are given the following expression to simplify:

(4x35x)+(8x3x3)(4x^3 - 5x) + (8x - 3x^3)

Let's break it down step by step:

  1. Group the like terms (terms with the same power of xx):

    • 4x33x34x^3 - 3x^3 (terms with x3x^3)
    • 5x+8x-5x + 8x (terms with xx)
  2. Simplify each group:

    • 4x33x3=x34x^3 - 3x^3 = x^3
    • 5x+8x=3x-5x + 8x = 3x
  3. Combine the results: x3+3xx^3 + 3x

Thus, the expression simplifies to:

x3+3xx^3 + 3x

The correct answer is A) x3+3xx^3 + 3x.

Would you like more details, or do you have any questions?

Here are 5 related questions to further explore this topic:

  1. How do you identify like terms in a polynomial expression?
  2. What are some strategies for simplifying polynomials with multiple variables?
  3. How do you factor a polynomial after simplifying it?
  4. What is the degree of the expression x3+3xx^3 + 3x?
  5. How would the process differ if there were fractional exponents?

Tip: Always start by grouping like terms when simplifying expressions—this makes the process much easier!

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Math Problem Analysis

Mathematical Concepts

Algebra
Polynomials
Like Terms

Formulas

Simplification of polynomials by combining like terms

Theorems

None explicitly used, but concept of combining like terms is fundamental

Suitable Grade Level

Grades 8-10