Which factor do $$ 9 x^{2}+30 x+25 $$ and $$ 9 x^{2}-25 $$ have in common? $$ 3 x+5 $$ $$ 3 x-5 $$ $$ 3 x+25 $$ $$ 9 x^{2} $$

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To determine the common factor between the two expressions $$ 9x^{2} + 30x + 25 $$ and $$ 9x^{2} - 25 $$, let's factor each expression separately.

1. **Factoring $$ 9x^{2} + 30x + 25 $$:**
   - This is a perfect square trinomial.
   - It can be written as:
     $$
     (3x + 5)^2 = 9x^{2} + 2 \cdot 3x \cdot 5 + 5^2 = 9x^{2} + 30x + 25
     $$
   - So, $$ 9x^{2} + 30x + 25 = (3x + 5)(3x + 5) $$.

2. **Factoring $$ 9x^{2} - 25 $$:**
   - This is a difference of squares.
   - It can be written as:
     $$
     (3x)^2 - 5^2 = (3x + 5)(3x - 5)
     $$
   - So, $$ 9x^{2} - 25 = (3x + 5)(3x - 5) $$.

**Common Factor:**
Both factored forms include the term $$ (3x + 5) $$. Therefore, the common factor is:

$$
\boxed{3 x + 5}
$$
The common factor is $$ 3x + 5 $$.

Which factor do \( 9 x^{2}+30 x+25 \) and \( 9 x^{2}-25 \) have in common? \( 3 x+5 \) \( 3 x-5 \) \( 3 x+25 \) \( 9 x^{2} \)

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