To find the product of [tex]\((3x + 5)(3x - 5)\)[/tex], we can use the difference of squares formula. The difference of squares states that:
[tex]\[
(a + b)(a - b) = a^2 - b^2
\][/tex]
In this case, let's identify [tex]\(a\)[/tex] and [tex]\(b\)[/tex] in our expression:
- [tex]\(a = 3x\)[/tex]
- [tex]\(b = 5\)[/tex]
Now, applying the difference of squares formula:
[tex]\[
(3x + 5)(3x - 5) = (3x)^2 - 5^2
\][/tex]
Next, we calculate each part:
[tex]\[
(3x)^2 = (3x) \cdot (3x) = 9x^2
\][/tex]
[tex]\[
5^2 = 5 \cdot 5 = 25
\][/tex]
Putting it all together:
[tex]\[
(3x + 5)(3x - 5) = 9x^2 - 25
\][/tex]
So, the product of [tex]\((3x + 5)(3x - 5)\)[/tex] is:
[tex]\[
9x^2 - 25
\][/tex]
Therefore, the correct answer is:
C. [tex]\(9x^2 - 25\)[/tex]
