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Let's solve the expression you provided, which is the subtraction of two polynomials:

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

To solve this, we first distribute the negative sign across the second polynomial and then combine like terms.

### Step-by-step Solution:
1. Distribute the negative sign to each term in the second polynomial:
   \[
   2x^3 - 3x^2 + 5x - 1 - (x^2 + 1 - 3x) = 2x^3 - 3x^2 + 5x - 1 - x^2 - 1 + 3x
   \]

2. Now, combine like terms:
   - \(x^3\) terms: \(2x^3\)
   - \(x^2\) terms: \(-3x^2 - x^2 = -4x^2\)
   - \(x\) terms: \(5x + 3x = 8x\)
   - Constant terms: \(-1 - 1 = -2\)

So the simplified result is:

\[
2x^3 - 4x^2 + 8x - 2
\]

This is the final answer after summing the polynomials vertically.

Would you like further details or clarifications?

Here are some related questions for practice:
1. What happens when we subtract two polynomials with more terms?
2. How do you solve a polynomial with negative exponents?
3. How do you factorize \(2x^3 - 4x^2 + 8x - 2\)?
4. What is the degree of the resulting polynomial?
5. How do you graph polynomials like \(2x^3 - 4x^2 + 8x - 2\)?

**Tip:** When adding or subtracting polynomials, always align like terms to avoid errors.

Suma los polinomios de forma vertical: (2x^3 - 3x^2 + 5x - 1) - (x^2 + 1 - 3x)

Learn how to subtract polynomials using the expression (2x^3 - 3x^2 + 5x - 1) - (x^2 + 1 - 3x). This problem involves combining like terms and understanding the properties of polynomial operations. Suitable for students in Grades 8-10.

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