Math Problem Statement

Simplify the following polynomial expression: (7x^2 + x - 8) - (-2x^2 - 8). Which expression is equivalent?

Solution

Let's simplify the given polynomial expression:

(7x2+x8)(2x28)\left( 7x^2 + x - 8 \right) - \left( -2x^2 - 8 \right)

Step-by-step solution:

  1. Distribute the negative sign in front of the second expression:

(7x2+x8)(2x28)=7x2+x8+2x2+8(7x^2 + x - 8) - (-2x^2 - 8) = 7x^2 + x - 8 + 2x^2 + 8

  1. Combine like terms:
    • For x2x^2 terms: 7x2+2x2=9x27x^2 + 2x^2 = 9x^2
    • For the constant terms: 8+8=0-8 + 8 = 0
    • For the linear term: xx remains as is.

So the simplified expression is:

9x2+x9x^2 + x

Final Answer:

The equivalent expression is 9x2+x9x^2 + x, which corresponds to option C.


Do you want more details on any step?
Here are some related questions:

  1. How do you distribute a negative sign over a polynomial?
  2. What are like terms and how do you combine them?
  3. How can we handle polynomials with multiple variables?
  4. What is the importance of simplifying expressions in algebra?
  5. Can polynomial expressions always be factored?

Tip: Always distribute negative signs carefully to avoid errors in simplifying polynomials.

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Math Problem Analysis

Mathematical Concepts

Algebra
Polynomials
Simplification

Formulas

(a - b) = a + (-b)
Combining like terms

Theorems

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Suitable Grade Level

Grades 8-10