To find the product of [tex]\((-3s + 2t)(4s - t)\)[/tex], let's proceed with a step-by-step expansion.
First, use the distributive property (also known as the FOIL method for binomials) to multiply each term in the first parenthesis by each term in the second parenthesis:
[tex]\[
(-3s + 2t)(4s - t)
\][/tex]
1. Multiply [tex]\(-3s\)[/tex] by [tex]\(4s\)[/tex]:
[tex]\[
-3s \cdot 4s = -12s^2
\][/tex]
2. Multiply [tex]\(-3s\)[/tex] by [tex]\(-t\)[/tex]:
[tex]\[
-3s \cdot -t = 3st
\][/tex]
3. Multiply [tex]\(2t\)[/tex] by [tex]\(4s\)[/tex]:
[tex]\[
2t \cdot 4s = 8st
\][/tex]
4. Multiply [tex]\(2t\)[/tex] by [tex]\(-t\)[/tex]:
[tex]\[
2t \cdot -t = -2t^2
\][/tex]
Now, combine all these products together:
[tex]\[
-12s^2 + 3st + 8st - 2t^2
\][/tex]
Next, combine like terms ([tex]\(3st\)[/tex] and [tex]\(8st\)[/tex]):
[tex]\[
-12s^2 + (3st + 8st) - 2t^2 = -12s^2 + 11st - 2t^2
\][/tex]
Therefore, the expanded product of [tex]\((-3s + 2t)(4s - t)\)[/tex] is:
[tex]\[
-12s^2 + 11st - 2t^2
\][/tex]
Out of the given choices, the correct answer is:
[tex]\[
\boxed{-12s^2 + 11st - 2t^2}
\][/tex]
