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The problem asks for an expression for the area of a square with side length given as \( 2x + 3 \), without using brackets and simplifying as much as possible.

### Solution:

The formula for the area of a square is:
\[
\text{Area} = \text{side}^2
\]

Given the side length is \( 2x + 3 \), the area will be:
\[
\text{Area} = (2x + 3)^2
\]

Now, expand the square:
\[
(2x + 3)^2 = (2x + 3)(2x + 3)
\]
Using the distributive property (FOIL method):
\[
(2x + 3)(2x + 3) = 2x(2x) + 2x(3) + 3(2x) + 3(3)
\]
Simplifying each term:
\[
= 4x^2 + 6x + 6x + 9
\]
Combine like terms:
\[
= 4x^2 + 12x + 9
\]

Thus, the simplified expression for the area of the square is:
\[
\boxed{4x^2 + 12x + 9}
\]

Let me know if you'd like further details or explanations!

### Follow-up Questions:
1. What would the expression for the perimeter of the square be?
2. How would the area expression change if the side length was \( 3x + 4 \)?
3. What are the roots of the expression \( 4x^2 + 12x + 9 = 0 \)?
4. How can you factorize \( 4x^2 + 12x + 9 \)?
5. How would the area formula change if the figure was a rectangle instead?

### Tip:
When expanding squared binomials like \( (a + b)^2 \), always apply the identity \( a^2 + 2ab + b^2 \) to simplify calculations.

Write an expression for the area of a square with side length 2x + 3, simplified as much as possible without using brackets.

Find the simplified expression for the area of a square with side length 2x + 3. This algebra problem involves expanding quadratic expressions and using basic geometry. Suitable for students in Grades 8-10.

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