Let's evaluate the algebraic expression $(x + y)^2 - 2z$ at $x = 2$, $y = 2$, and $z = -2$.

Step-by-step:

1. Substitute $x = 2$, $y = 2$, and $z = -2$ into the expression: $(x + y)^2 - 2z = (2 + 2)^2 - 2(-2)$
2. Simplify the terms inside the parentheses: $(2 + 2) = 4$ So the expression becomes: $4^2 - 2(-2)$
3. Simplify the powers and multiplication: $4^2 = 16 \quad \text{and} \quad -2(-2) = 4$ So the expression is now: $16 + 4$
4. Add the results: $16 + 4 = 20$

Final Answer:

$\boxed{20}$

Would you like any further details or explanations?

Here are 5 related questions to expand your understanding:

1. How would the result change if $z = 2$ instead of $-2$?
2. What happens if we change the exponent from 2 to 3 in the expression $(x + y)^2$?
3. Can you simplify the general expression $(x + y)^2 - 2z$ without specific values for $x$, $y$, and $z$?
4. How would the result change if you evaluated $(x - y)^2 - 2z$ instead?
5. How does this expression behave for negative values of $x$ and $y$?

Tip: Always simplify inside parentheses first when solving expressions involving multiple operations!