To determine the correct product of [tex]\((7x - 3)(7x + 3)\)[/tex], we need to recognize that this is a special binomial product known as the difference of squares.
The difference of squares states that:
[tex]\[
(a - b)(a + b) = a^2 - b^2
\][/tex]
Here, [tex]\(a = 7x\)[/tex] and [tex]\(b = 3\)[/tex]. Applying the difference of squares formula, we get:
[tex]\[
(7x - 3)(7x + 3) = (7x)^2 - (3)^2
\][/tex]
Now, we need to compute each squared term:
1. [tex]\((7x)^2\)[/tex]:
[tex]\[
(7x)^2 = 7^2 \cdot x^2 = 49x^2
\][/tex]
2. [tex]\((3)^2\)[/tex]:
[tex]\[
(3)^2 = 9
\][/tex]
Putting these results together, we have:
[tex]\[
(7x - 3)(7x + 3) = 49x^2 - 9
\][/tex]
Therefore, the correct product of [tex]\((7x - 3)(7x + 3)\)[/tex] is:
[tex]\[
49x^2 - 9
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{49x^2 - 9}
\][/tex]
