Question

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Explanation:

1. The trinomial $x^2 + 6x + 9$ fits the form $(a+b)^2 = a^2 + 2ab + b^2$, so it is a perfect square trinomial.
2. Perfect square trinomials follow a predictable factoring pattern that simplifies algebra and quadratic solutions.
3. The equation $x^2 + 2mx + m^2$ matches the standard perfect square trinomial structure $(x+m)^2$.
4. In the standard quadratic trinomial $ax^2 + bx + c$ that is a perfect square, $b = 2\sqrt{a}\sqrt{c}$, meaning $b$ is twice the product of the square roots of $a$ and $c$.

Answer:

1. perfect square
2. perfect square
3. perfect square
4. twice