Simplify (5*x*3 + 7*x* – 8) + (2*x*3 – 5*x*2 – *x*).


To simplify the expression \((5x^3 + 7x - 8) + (2x^3 - 5x^2 - x)\), we will first remove the parentheses and then combine like terms.

### Step 1: Remove the parentheses
\[
5x^3 + 7x - 8 + 2x^3 - 5x^2 - x
\]

### Step 2: Combine like terms
- Combine the \(x^3\) terms: \(5x^3 + 2x^3 = 7x^3\)
- Combine the \(x^2\) terms: There's only \(-5x^2\)
- Combine the \(x\) terms: \(7x - x = 6x\)
- Combine the constant terms: \(-8\) (no other constant term to combine with)

### Final Simplified Expression
\[
7x^3 - 5x^2 + 6x - 8
\]

So, the simplified expression is \(7x^3 - 5x^2 + 6x - 8\).

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Do you want more details or have any questions? Here are 5 related questions that could expand your understanding:

1. How do you identify like terms in a polynomial expression?
2. What are the steps to simplify a polynomial expression involving subtraction?
3. How would the expression change if one of the coefficients were negative?
4. What does the degree of the simplified polynomial tell us about its graph?
5. How would you factor the simplified polynomial if required?

**Tip:** Always arrange terms by descending powers of \(x\) when simplifying polynomial expressions to maintain clarity.

Learn how to simplify the polynomial expression 5x^3 + 7x - 8 + 2x^3 - 5x^2 - x step-by-step with detailed explanations. This problem involves polynomial simplification and combining like terms, suitable for students in Grades 9-12.

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