Factor the perfect square trinomials. Write your answer in the form of (a+b)2

To factor the perfect square trinomials, we can use the formulas:

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

Now we will factor each trinomial:

1) **\(x^2 + 6x + 9\)**
We recognize this as the expansion of \((x + 3)^2\).

\[
x^2 + 6x + 9 = (x + 3)^2
\]

2) **\(x^2 + 10x + 25\)**
This is the expansion of \((x + 5)^2\).

\[
x^2 + 10x + 25 = (x + 5)^2
\]

3) **\(9x^2 + 12x + 4\)**
This can be factored as \((3x + 2)^2\).

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

4) **\(9x^2 - 30x + 25\)**
This can be factored as \((3x - 5)^2\).

\[
9x^2 - 30x + 25 = (3x - 5)^2
\]

Putting it all together, the factored forms of the given perfect square trinomials are:

1) \( (x + 3)^2 \)
2) \( (x + 5)^2 \)
3) \( (3x + 2)^2 \)
4) \( (3x - 5)^2 \)