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.