Which factor do 64x^2+48x+9

To find a common factor between the two expressions \(64x^2 + 48x + 9\) and \(64x^2 - 9\), we can try to determine if they share any factors via factoring or looking for common terms.

1. **Factor the first expression \(64x^2 + 48x + 9\)**.

To factor this quadratic expression \(64x^2 + 48x + 9\), we can use the quadratic formula or look for perfect squares, but let's first check if it can be factorized neatly.

The coefficients suggest that it may be factorable:

\[
64x^2 + 48x + 9 = (8x + 3)(8x + 3) = (8x + 3)^2
\]

So, we have:

\[
64x^2 + 48x + 9 = (8x + 3)^2
\]

2. **Factor the second expression \(64x^2 - 9\)**.

This expression is a difference of squares:

\[
64x^2 - 9 = (8x)^2 - 3^2 = (8x - 3)(8x + 3)
\]

3. **Common factors**:

Now, we look at both factored forms:

- The first expression, \(64x^2 + 48x + 9\), factors to \((8x + 3)^2\)
- The second expression, \(64x^2 - 9\), factors to \((8x - 3)(8x + 3)\)

From these forms, we can see that both expressions share a common factor of \(8x + 3\).

Hence, the common factor between \(64x^2 + 48x + 9\) and \(64x^2 - 9\) is:

\[
\boxed{8x + 3}
\]