https://file.aiquickdraw.com/mathbot/file/17240368812149roma5zi.jpg

Evaluate the following expression. Choose the correct answer among the given choices.

Let's simplify the given expression:

\[
(2x^3 - 4x^2 + 6x - 8) + (-x^3 + 5x^2 - 3x + 1)
\]

To do this, we combine like terms:

1. Combine the \(x^3\) terms:
   \[
   2x^3 + (-x^3) = x^3
   \]

2. Combine the \(x^2\) terms:
   \[
   -4x^2 + 5x^2 = x^2
   \]

3. Combine the \(x\) terms:
   \[
   6x + (-3x) = 3x
   \]

4. Combine the constant terms:
   \[
   -8 + 1 = -7
   \]

Thus, the simplified expression is:

\[
x^3 + x^2 + 3x - 7
\]

Now, let's check which option matches this expression. The correct answer is:

**A) \(x^3 + x^2 + 3x - 7\)**

Would you like further details or explanations?

---

Here are some related questions for further practice:

1. How would you simplify the expression \((3x^3 - 2x^2 + x - 4) + (x^3 + 4x^2 - 3x + 2)\)?
2. What is the result of subtracting \((2x^3 + 3x^2 - 5x + 6)\) from \((4x^3 - x^2 + 7x - 1)\)?
3. How do you expand and simplify \((x - 2)(2x^2 + 3x - 1)\)?
4. What is the general approach to combining polynomials of different degrees?
5. If the expression was \((5x^3 - 4x + 2) + (-3x^3 + x^2 - 6x)\), what would the simplified form be?

**Tip:** When adding or subtracting polynomials, ensure each term is aligned with its like term (same degree) to avoid errors.

Learn how to evaluate and simplify the polynomial expression: 2x^3 - 4x^2 + 6x - 8 + (-x^3 + 5x^2 - 3x + 1). Understand the process of combining like terms to simplify polynomials. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation