To evaluate the expression \((2x + 3)^2\), we need to apply the formula for the square of a binomial, which is:

\[
(a + b)^2 = a^2 + 2ab + b^2
\]

Here, \(a = 2x\) and \(b = 3\).

### Step-by-Step Solution:

1. **Square the first term \(a^2\):**
   \[
   (2x)^2 = 4x^2
   \]

2. **Multiply the first and second terms and double it \(2ab\):**
   \[
   2 \times (2x) \times 3 = 12x
   \]

3. **Square the second term \(b^2\):**
   \[
   3^2 = 9
   \]

### Combine all the terms:

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

So, the evaluated expression is:

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

Would you like to go deeper into any part of this solution or have other related questions?

### Relative Questions
1. How do you expand binomials with higher powers?
2. What is the difference between binomial expansion and polynomial expansion?
3. How does the distributive property help in expanding algebraic expressions?
4. Can you explain the square of a binomial using a geometric approach?
5. How can binomial expansion be used in probability?

**Tip:** Memorizing key algebraic identities, like \((a + b)^2\), can greatly speed up solving such problems.

Learn how to evaluate the expression (2x + 3)^2 with a detailed step-by-step solution. Understand the application of the square of a binomial formula (a + b)^2 = a^2 + 2ab + b^2. Suitable for students in Grades 7-9.

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