Factor the following trinomial. $$ \begin{array}{l}25 x^{2}+30 x+9 \ ([?] x+\square)^{2}\end{array} $$

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UpStudy AI · Accepted Answer

To factor the trinomial $$25x^{2} + 30x + 9$$ as a perfect square, follow these steps:

1. **Identify the Square Terms:**
   - $$25x^{2}$$ is the square of $$5x$$.
   - $$9$$ is the square of $$3$$.

2. **Check the Middle Term:**
   - A perfect square trinomial has the form $$(ax + b)^2 = a^2x^2 + 2abx + b^2$$.
   - Here, $$2abx = 2 \times 5x \times 3 = 30x$$, which matches the middle term of the trinomial.

3. **Write the Factored Form:**
   - Since all parts fit the perfect square pattern, the trinomial can be written as $$(5x + 3)^2$$.

**Final Answer:**
$$
(5x + 3)^{2}
$$
$$ (5x + 3)^2 $$

Factor the following trinomial.

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