Factor the perfect square trinomial: $$ x^{2} + 12x + 36 $$

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The given trinomial is:

$$ x^{2} + 12x + 36 $$

To factor this as a perfect square trinomial, we look for a binomial of the form $$(x + a)^2$$ that expands to the given trinomial.

1. **Identify the square terms:**
   - The first term $$x^{2}$$ is already a perfect square.
   - The last term $$36$$ is a perfect square, since $$6^2 = 36$$.

2. **Determine the middle term:**
   - In $$(x + a)^2$$, the middle term is $$2ax$$.
   - Here, the middle term is $$12x$$, so $$2a = 12$$.
   - Solving for $$a$$ gives $$a = 6$$.

3. **Write the factored form:**
   - Substitute $$a = 6$$ into the binomial:
     $$
     (x + 6)^2
     $$

**Final Answer:**

$$ (x + 6)^{2} $$
$$ (x + 6)^2 $$

Factor the perfect square trinomial:

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