To determine the correct product of [tex]\((3x - 8)^2\)[/tex], let's expand the expression step by step using the binomial theorem or the formula for the square of a binomial, which is given by:
[tex]\[
(a - b)^2 = a^2 - 2ab + b^2
\][/tex]
Here, [tex]\(a = 3x\)[/tex] and [tex]\(b = 8\)[/tex].
1. Square the first term ([tex]\(a^2\)[/tex]):
[tex]\[
(3x)^2 = 9x^2
\][/tex]
2. Multiply the two terms together and double the product ([tex]\(-2ab\)[/tex]):
[tex]\[
-2 \cdot (3x) \cdot 8 = -48x
\][/tex]
3. Square the second term ([tex]\(b^2\)[/tex]):
[tex]\[
8^2 = 64
\][/tex]
Combining all these terms, we get:
[tex]\[
9x^2 - 48x + 64
\][/tex]
So, the correct product of [tex]\((3x - 8)^2\)[/tex] is:
[tex]\[
9x^2 - 48x + 64
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{9x^2 - 48x + 64}
\][/tex]
