Cho A = (x+5y)(x-5y) - (x+2)² + 4z + 25y²

To simplify the expression \( A = (x + 5y)(x - 5y) - (x + 2)^2 + 4z + 25y^2 \), we can proceed as follows:

1. **Expand the terms:**
- The product \( (x + 5y)(x - 5y) \) is a difference of squares:
\[
(x + 5y)(x - 5y) = x^2 - (5y)^2 = x^2 - 25y^2
\]

- Expand \( -(x + 2)^2 \):
\[
-(x + 2)^2 = - (x^2 + 4x + 4) = -x^2 - 4x - 4
\]

2. **Substitute these expansions back into \( A \):**
\[
A = (x^2 - 25y^2) - (x^2 + 4x + 4) + 4z + 25y^2
\]

3. **Combine like terms:**
- Combine the \( x^2 \) terms:
\[
x^2 - x^2 = 0
\]
- Combine the \( y^2 \) terms:
\[
-25y^2 + 25y^2 = 0
\]
- Now, we only have the linear and constant terms left:
\[
A = -4x - 4 + 4z
\]

4. **Final simplified form:**
Thus, the expression simplifies to:
\[
A = 4z - 4x - 4
\]

For the other parts, like proving that \( A \) does not depend on the variables \( x \) and \( y \), you would show that the simplified expression does not include \( y \) or relate to \( x \) after simplification.

If you have specific questions about the next parts of your problem or need help with other concepts, feel free to ask!