Let's determine the product of the given expressions step by step:
Given expressions:
[tex]\[
(9t - 4)(-9t - 4)
\][/tex]
We'll use the distributive property, also known as the FOIL method (First, Outer, Inner, Last), to expand this expression.
1. First terms: Multiply the first terms in each expression.
[tex]\[
9t \cdot (-9t) = -81t^2
\][/tex]
2. Outer terms: Multiply the outer terms in the expression.
[tex]\[
9t \cdot (-4) = -36t
\][/tex]
3. Inner terms: Multiply the inner terms.
[tex]\[
-4 \cdot (-9t) = 36t
\][/tex]
4. Last terms: Multiply the last terms in each expression.
[tex]\[
-4 \cdot (-4) = 16
\][/tex]
Now, we sum up all these terms:
[tex]\[
-81t^2 + (-36t) + 36t + 16
\][/tex]
Combine the like terms ([tex]\(-36t + 36t\)[/tex]):
[tex]\[
-81t^2 + 0t + 16
\][/tex]
We can simplify this to:
[tex]\[
-81t^2 + 16
\][/tex]
Therefore, the correct answer is:
[tex]\[
-81t^2 + 16
\][/tex]
So, the correct choice from the given options is:
[tex]\[
-81t^2 + 16
\][/tex]
