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The problem asks to find an expression for the area of a square, where the side length is given as \(3x + 4\). 

The area \(A\) of a square is calculated using the formula:

\[
A = \text{side}^2
\]

Substitute the given side length:

\[
A = (3x + 4)^2
\]

Now, we expand this expression using the formula for the square of a binomial:

\[
(3x + 4)^2 = (3x)^2 + 2(3x)(4) + 4^2
\]

Simplify each term:

\[
(3x)^2 = 9x^2, \quad 2(3x)(4) = 24x, \quad 4^2 = 16
\]

Thus, the expanded form is:

\[
A = 9x^2 + 24x + 16
\]

Therefore, the expression for the area of the square is:

\[
A = 9x^2 + 24x + 16
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How would the expression change if the side length was \(4x - 5\)?
2. What is the perimeter of the square with side length \(3x + 4\)?
3. How do you factor the quadratic expression \(9x^2 + 24x + 16\)?
4. How does the area formula change if the shape is a rectangle instead of a square?
5. Can you solve \(9x^2 + 24x + 16 = 100\) for \(x\)?

**Tip:** When squaring a binomial, always apply the formula \((a + b)^2 = a^2 + 2ab + b^2\).

Write an expression for the area of the square below. Your expression should not have any brackets and should be written as simply as possible.

Learn how to simplify the expression for the area of a square with a side length of 3x + 4. This math problem covers algebraic concepts such as binomial expansion and simplifying quadratic expressions. Suitable for Grades 8-10 students.

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