The expression given is:

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

Let's simplify it step by step:

1. Distribute the negative sign across the second set of parentheses:
\[
= 3x - 1 - 4 - x^2
\]

2. Combine like terms:
\[
= -x^2 + 3x - 5
\]

Thus, the simplified expression is:

\[
-x^2 + 3x - 5
\]

Would you like further details or have any questions?

Here are 5 related questions to expand on this topic:
1. How do you simplify expressions with multiple parentheses?
2. What are like terms, and how do you combine them?
3. How can you factor quadratic expressions like \( -x^2 + 3x - 5 \)?
4. How would the process change if the expression was \( (3x - 1) - (4 - x^2) \)?
5. How do you solve a quadratic equation derived from an expression like this?

**Tip:** Always pay attention to negative signs when distributing across parentheses. It can change the entire expression!

Learn how to simplify the algebraic expression (3x-1)-(4+x^2) step-by-step. This guide covers the application of the distributive property and combining like terms to reach the final simplified expression -x^2 + 3x - 5. Suitable for students in Grades 8-10.

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