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The given expression is:

\[
(2x - 3)^2 - (x + 1)^2
\]

Let's simplify this step by step.

### Step 1: Expand each squared term.

\[
(2x - 3)^2 = (2x - 3)(2x - 3) = 4x^2 - 6x - 6x + 9 = 4x^2 - 12x + 9
\]
\[
(x + 1)^2 = (x + 1)(x + 1) = x^2 + x + x + 1 = x^2 + 2x + 1
\]

### Step 2: Subtract the second expanded term from the first.

\[
(4x^2 - 12x + 9) - (x^2 + 2x + 1)
\]

Distribute the negative sign:

\[
4x^2 - 12x + 9 - x^2 - 2x - 1
\]

### Step 3: Combine like terms.

\[
(4x^2 - x^2) + (-12x - 2x) + (9 - 1)
\]
\[
= 3x^2 - 14x + 8
\]

### Final Simplified Expression:

\[
3x^2 - 14x + 8
\]

This is the simplified form of the given expression.

Would you like any further clarification?

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Here are 5 related questions you might want to explore:
1. How do you simplify more complex polynomial expressions?
2. What is the difference of squares, and how does it apply here?
3. How do you solve quadratic equations after simplification?
4. What happens if you factor the final expression \(3x^2 - 14x + 8\)?
5. Can this expression be applied to any real-world scenarios?

**Tip:** When dealing with squared binomials, expanding them carefully step by step helps avoid common mistakes!

Learn how to simplify the expression (2x - 3)^2 - (x + 1)^2 step-by-step. This problem involves key algebraic concepts such as the square of a binomial and the difference of squares. Suitable for students in Grades 9-11.

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