Let's simplify the given expression:

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

### Step 1: Distribute the negative sign across the second polynomial
\[
3x^2 + 4x + 1 - 4x^4 - x - 3
\]

### Step 2: Combine like terms
- The \(4x^4\) term stands alone.
- Combine \(3x^2\), which has no like term.
- Combine \(4x - x = 3x\).
- Combine the constants \(1 - 3 = -2\).

### Final simplified expression:
\[
-4x^4 + 3x^2 + 3x - 2
\]

Let me know if you'd like further details or explanations!

Here are 5 questions to expand on this:

1. How do you identify and combine like terms in polynomial expressions?
2. What are the different types of polynomials based on degree?
3. How does the degree of a polynomial affect its graph?
4. Can polynomials have negative exponents?
5. What are some common techniques for factoring polynomials?

**Tip:** When simplifying expressions, always ensure all signs are correctly applied before combining like terms!

Learn how to simplify the polynomial expression (3x^2 + 4x + 1) - (4x^4 + x + 3) with step-by-step guidance. This problem involves combining like terms and performing polynomial subtraction, covering key algebraic concepts suitable for Grades 8-10.

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