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The expression provided is:

\[
-6 - 2y^2 + 6x - 4x + 1 + 7y^2 - y^2
\]

Let's simplify it by combining like terms.

### Step 1: Combine the terms with \( y^2 \)
The terms involving \( y^2 \) are:
\[
-2y^2 + 7y^2 - y^2
\]
Simplifying these, we get:
\[
(-2 + 7 - 1)y^2 = 4y^2
\]

### Step 2: Combine the terms with \( x \)
The terms involving \( x \) are:
\[
6x - 4x
\]
Simplifying these, we get:
\[
(6 - 4)x = 2x
\]

### Step 3: Combine the constant terms
The constant terms are:
\[
-6 + 1
\]
Simplifying these, we get:
\[
-6 + 1 = -5
\]

### Final Simplified Expression
Putting it all together, the simplified expression is:
\[
4y^2 + 2x - 5
\]

Would you like further details or have any questions?

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Here are some related questions:
1. What is the degree of the simplified expression?
2. Can we factorize this expression further?
3. How would this expression change if we added another variable?
4. What is the result if \( y = 1 \) and \( x = 2 \) in the simplified expression?
5. What would be the result if the constant term was changed?

**Tip:** Always check for like terms carefully to ensure accurate simplification.

Learn how to simplify the algebraic expression -6 - 2y^2 + 6x - 4x + 1 + 7y^2 - y^2 by combining like terms. This problem is suitable for students in Grades 7-8, covering key algebra concepts and simplification techniques.

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