Let's simplify the expression step by step:

Expression:  
\[
4x^2 - 2x + 3 + 3x^2 + 5x - 4
\]

1. Combine the like terms (terms with \(x^2\), terms with \(x\), and constants):
   - \(x^2\) terms: \(4x^2 + 3x^2 = 7x^2\)
   - \(x\) terms: \(-2x + 5x = 3x\)
   - Constant terms: \(3 - 4 = -1\)

Thus, the simplified expression is:
\[
7x^2 + 3x - 1
\]

Would you like more details on combining terms or further clarification?

Here are five related questions you might find interesting:
1. How do you factor quadratic expressions like \(7x^2 + 3x - 1\)?
2. What is the discriminant, and how does it relate to solving quadratic equations?
3. How do you solve a quadratic equation using the quadratic formula?
4. What are the properties of a parabola represented by \(7x^2 + 3x - 1\)?
5. How can you complete the square for the expression \(7x^2 + 3x - 1\)?

**Tip:** Always group similar terms (like powers of \(x\)) to simplify algebraic expressions efficiently.

Learn how to simplify the polynomial expression 4x^2 - 2x + 3 + 3x^2 + 5x - 4 by combining like terms. This problem focuses on algebraic concepts, including polynomial simplification and combining terms, suitable for students in Grades 7-9.

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