Step-by-step explanation:

First of all, you need to factor the expression

4x² +12x + 9

This will be a trial and error method.

Since you have a given choice, it will be obvious to know the right answer. We are talking about squares here

So

(2x + 3) will be the right one. Since only the 2x times itself will give us 4x^2

Remember Area of square is equal to side squared. or A = a^2

let's check:

2x + 3

2x + 3

-------------------

6x + 9 -> (2x + 3) * 3

4x^2 + 6x -> (2x + 3) * 2x

-------------------

4x^2 + 12x + 9 -> correct