To simplify the expression \((3x^2 - 18x + 40x^3 - 25x^4 + 4x^5) + (x^2 - 6x + 9)\), we combine like terms.

### Step 1: Write down the expression
\[
(3x^2 - 18x + 40x^3 - 25x^4 + 4x^5) + (x^2 - 6x + 9)
\]

### Step 2: Combine like terms
- **\(x^5\) term**: \(4x^5\)
- **\(x^4\) term**: \(-25x^4\)
- **\(x^3\) term**: \(40x^3\)
- **\(x^2\) terms**: \(3x^2 + x^2 = 4x^2\)
- **\(x\) terms**: \(-18x - 6x = -24x\)
- **Constant term**: \(9\)

### Step 3: Write the final simplified expression
\[
4x^5 - 25x^4 + 40x^3 + 4x^2 - 24x + 9
\]

This is the simplified expression after combining all the like terms.

Would you like any additional details or explanations?

### Related Questions:
1. How do you combine like terms in polynomial expressions?
2. What is the degree of a polynomial and how is it determined?
3. How do you add and subtract polynomials?
4. Can polynomials be simplified further by factoring?
5. What are the common mistakes to avoid when combining polynomials?

### Tip:
When simplifying polynomials, always align like terms vertically to avoid missing any terms during addition or subtraction.

Learn how to simplify the polynomial expression 3x^2 - 18x + 40x^3 - 25x^4 + 4x^5 + x^2 - 6x + 9 with a step-by-step solution. This problem covers polynomial arithmetic and combining like terms. Suitable for students in Grades 7-9.

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