Let's simplify the given expression:

\[
(2x + 5)^2 - 2(2x + 5)
\]

### Step 1: Expand \((2x + 5)^2\)
We use the formula for squaring a binomial \((a + b)^2 = a^2 + 2ab + b^2\):

\[
(2x + 5)^2 = (2x)^2 + 2(2x)(5) + 5^2 = 4x^2 + 20x + 25
\]

### Step 2: Expand \(- 2(2x + 5)\)
Distribute the \(-2\):

\[
-2(2x + 5) = -2 \cdot 2x - 2 \cdot 5 = -4x - 10
\]

### Step 3: Combine the results
Now, combine the expanded terms:

\[
(4x^2 + 20x + 25) + (-4x - 10)
\]

Simplify by combining like terms:

\[
4x^2 + (20x - 4x) + (25 - 10) = 4x^2 + 16x + 15
\]

Thus, the simplified expression is:

\[
4x^2 + 16x + 15
\]

Let me know if you'd like more details on this! 

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Here are 5 follow-up questions based on this:

1. What is the factored form of the expression \(4x^2 + 16x + 15\)?
2. Can we solve \(4x^2 + 16x + 15 = 0\) using the quadratic formula?
3. How would the expansion differ if the original expression was \((2x - 5)^2 - 2(2x - 5)\)?
4. What are the roots of the quadratic equation formed from this expression?
5. How does completing the square work on \(4x^2 + 16x + 15\)?

**Tip:** Always expand expressions step by step to avoid errors with signs or coefficients!

Explore how to simplify the algebraic expression (2x+5)^2 - 2(2x+5) using binomial expansion and distribution techniques. This guide is perfect for students in Grades 8-10 who want to understand polynomial operations and algebraic manipulation.

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