Let's simplify the given expression step by step:

The given expression is:

$x^2 + 4x + 4 + y^2 - 2y + 1 - x^2 - 2x + 1 - y^2 - 6y - 1$

Step 1: Group like terms

Separate terms involving $x^2$, $x$, $y^2$, $y$, and constants:

$(x^2 - x^2) + (4x - 2x) + (y^2 - y^2) + (-2y - 6y) + (4 + 1 + 1 - 1)$

Step 2: Simplify each group

• $x^2 - x^2 = 0$
• $4x - 2x = 2x$
• $y^2 - y^2 = 0$
• $-2y - 6y = -8y$
• $4 + 1 + 1 - 1 = 5$

Step 3: Combine the results

$0 + 2x + 0 - 8y + 5 = 2x - 8y + 5$

Final Simplified Expression:

$2x - 8y + 5$

Let me know if you would like further clarification or assistance!

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Related Questions:

1. What is the difference between combining like terms and factoring?
2. How can I represent this simplified expression graphically?
3. What role do constants play in equations like these?
4. How do coefficients affect the behavior of terms in an equation?
5. How do you identify like terms in a polynomial expression?

Tip:

When simplifying expressions, carefully group and simplify each term step by step to avoid mistakes.