Evaluate the following algebraic expression at x=2
, y=2
, z=−2
 and simplify your answer.

(x+y)2−2z

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!

Evaluate the following algebraic expression at x=2, y=2, z=−2 and simplify your answer: (x+y)^2−2z

Discover how to evaluate and simplify the algebraic expression (x+y)^2−2z when x=2, y=2, and z=-2. This step-by-step solution covers core algebraic concepts, exponentiation, and substitution. Perfect for students in Grades 6-8 looking to strengthen their algebra skills.

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