Expand (3x+4)²: Perfect Square Binomial Expression

To solve the problem $(3x + 4)^2$, we will use the formula for the square of a binomial:

$(a + b)^2 = a^2 + 2ab + b^2$

• Identify $a$ and $b$: Here, $a = 3x$ and $b = 4$.
• Apply the formula:

1. Calculate $a^2$ which is $(3x)^2 = 9x^2$.

2. Calculate $2ab$ which is $2 \times (3x) \times 4 = 24x$.

3. Calculate $b^2$ which is $4^2 = 16$.

Combine the results:

• $a^2 + 2ab + b^2 = 9x^2 + 24x + 16$.

Therefore, the expanded form of $(3x + 4)^2$ is $9x^2 + 24x + 16$.

The correct answer choice is: $9x^2 + 24x + 16$.