https://file.aiquickdraw.com/mathbot/file/1725557082033b6c38ixp.jpg

The expression in the image is:

\[
(4x^2 - 2) - (6x + 1) - (x^2 - 5)
\]

Let's simplify it step by step:

1. Distribute the negative signs through each term inside the parentheses:
\[
4x^2 - 2 - 6x - 1 - x^2 + 5
\]

2. Combine like terms:
   - For the \(x^2\) terms: \(4x^2 - x^2 = 3x^2\)
   - For the constant terms: \(-2 - 1 + 5 = 2\)
   - For the \(x\) term: \(-6x\)

So, the simplified expression is:

\[
3x^2 - 6x + 2
\]

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. What is the degree of the simplified polynomial?
2. Can you factor the quadratic expression \(3x^2 - 6x + 2\)?
3. How would the expression change if the sign of one of the terms were different?
4. What is the vertex form of this quadratic expression?
5. How can you find the roots of \(3x^2 - 6x + 2\) using the quadratic formula?

**Tip:** Always distribute negative signs carefully to avoid errors in simplifying expressions!

Learn how to simplify the polynomial expression (4x^2 - 2) - (6x + 1) - (x^2 - 5) with a step-by-step breakdown. This problem demonstrates algebraic techniques such as the distributive property and combining like terms, suitable for students in Grades 8-10.

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