Let's solve the given expression:

The expression is \( 5(3x + 2)^2 \).

### Step-by-Step Solution:

1. First, recognize that \( (3x + 2)^2 \) is a binomial squared. Use the binomial expansion formula:
   \[
   (a + b)^2 = a^2 + 2ab + b^2
   \]
   Here, \( a = 3x \) and \( b = 2 \). Now apply the formula:
   \[
   (3x + 2)^2 = (3x)^2 + 2(3x)(2) + 2^2
   \]
   Simplifying each term:
   \[
   (3x)^2 = 9x^2, \quad 2(3x)(2) = 12x, \quad 2^2 = 4
   \]
   So,
   \[
   (3x + 2)^2 = 9x^2 + 12x + 4
   \]

2. Now multiply this result by 5:
   \[
   5(9x^2 + 12x + 4) = 5 \cdot 9x^2 + 5 \cdot 12x + 5 \cdot 4
   \]
   Simplify each term:
   \[
   5 \cdot 9x^2 = 45x^2, \quad 5 \cdot 12x = 60x, \quad 5 \cdot 4 = 20
   \]

3. Therefore, the fully expanded expression is:
   \[
   45x^2 + 60x + 20
   \]

### Final Answer:
\[
45x^2 + 60x + 20
\]

Would you like more details or have any questions?

Here are 5 related questions to practice:
1. Expand and simplify \( 4(2x + 5)^2 \).
2. Expand \( 7(5x - 3)^2 \).
3. Factor \( 12x^2 + 24x + 12 \).
4. What is the derivative of \( 3x^2 + 6x + 9 \)?
5. Solve \( 2(4x + 1)^2 = 0 \).

**Tip:** When expanding binomials, always apply the distributive property carefully, especially with squared terms.

Learn how to expand and simplify the expression 5(3x + 2)^2 using binomial expansion. This detailed solution covers key algebraic concepts, including the binomial expansion formula and the distributive property. Suitable for students in Grades 9-11.

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