Sure, let's evaluate the expression \(3x^2 - 2xy - 4y^2\) step by step given \(x = 2\) and \(y = -3\).
1. Substitute the given values of \(x\) and \(y\) into the expression:
[tex]\[
3(2)^2 - 2(2)(-3) - 4(-3)^2
\][/tex]
2. Calculate each term separately:
- First term: \(3(2)^2 = 3 \cdot 4 = 12\)
- Second term: \(-2(2)(-3) = -2 \cdot 2 \cdot -3 = 4 \cdot 3 = 12\)
- Third term: \(-4(-3)^2 = -4 \cdot 9 = -36\)
3. Combine all the terms:
[tex]\[
12 + 12 - 36
\][/tex]
4. Simplify the result:
[tex]\[
12 + 12 = 24
\][/tex]
[tex]\[
24 - 36 = -12
\][/tex]
Therefore, the value of the expression [tex]\(3x^2 - 2xy - 4y^2\)[/tex] when [tex]\(x = 2\)[/tex] and [tex]\(y = -3\)[/tex] is [tex]\(-12\)[/tex]. So, the correct answer is [tex]\(\boxed{-12}\)[/tex].
