Answer :

Let's find the product step-by-step:

First, given the two expressions:
[tex]\[ (9t - 4) \][/tex]
and
[tex]\[ (-9t - 4) \][/tex]

We need to calculate the product of these two expressions:
[tex]\[ (9t - 4)(-9t - 4) \][/tex]

To multiply these expressions, we apply the distributive property (also known as the FOIL method for binomials):

1. First terms:
[tex]\[ 9t \times (-9t) = -81t^2 \][/tex]

2. Outer terms:
[tex]\[ 9t \times (-4) = -36t \][/tex]

3. Inner terms:
[tex]\[ -4 \times (-9t) = 36t \][/tex]

4. Last terms:
[tex]\[ -4 \times (-4) = 16 \][/tex]

Now, let's combine all these terms:
[tex]\[ -81t^2 - 36t + 36t + 16 \][/tex]

Notice that the middle terms \(-36t\) and \(36t\) cancel each other out:
[tex]\[ -81t^2 + 16 \][/tex]

Therefore, the product of \((9t - 4)(-9t - 4)\) is:
[tex]\[ -81t^2 + 16 \][/tex]

Among the given options, the correct answer is:
[tex]\[ -81t^2 + 16 \][/tex]