Let's solve the given expression step by step:

The expression is:

\[
|2 - 5| - \left( \frac{6}{2} + 1 \right)^2
\]

### Step 1: Simplify the absolute value part
First, calculate the absolute value:

\[
|2 - 5| = |-3| = 3
\]

So, the expression becomes:

\[
3 - \left( \frac{6}{2} + 1 \right)^2
\]

### Step 2: Simplify inside the parentheses
Next, simplify \(\frac{6}{2} + 1\):

\[
\frac{6}{2} = 3
\]

\[
3 + 1 = 4
\]

So now, the expression is:

\[
3 - 4^2
\]

### Step 3: Square the 4
\[
4^2 = 16
\]

### Step 4: Final calculation
Now subtract:

\[
3 - 16 = -13
\]

### Final Answer:
\[
\boxed{-13}
\]

Would you like further clarification on any step? Here are some related problems for practice:

1. \(|7 - 12| - \left(\frac{8}{4} + 2\right)^2\)
2. \(|4 - 9| - \left(\frac{10}{5} + 3\right)^2\)
3. \(|5 - 3| - \left(\frac{9}{3} + 4\right)^2\)
4. \(|10 - 15| - \left(\frac{12}{6} + 5\right)^2\)
5. \(|8 - 2| - \left(\frac{14}{7} + 6\right)^2\)

**Tip:** Always solve operations inside parentheses and apply exponents before handling addition or subtraction outside.

Learn how to solve the expression |2-5|-(6/2+1)^2 using absolute value, order of operations, and exponents. This step-by-step solution is ideal for students in Grades 6-8, helping them understand key concepts in arithmetic and algebra.

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