To determine which expression is equivalent to [tex]\(-3x(x-4) - 2x(x+3)\)[/tex], let’s simplify it step-by-step.
1. Start with the original expression:
[tex]\[
-3x(x - 4) - 2x(x + 3)
\][/tex]
2. Distribute each term inside the parentheses:
[tex]\[
-3x(x - 4) = -3x^2 + 12x
\][/tex]
[tex]\[
-2x(x + 3) = -2x^2 - 6x
\][/tex]
3. Combine these two results to form a single expression:
[tex]\[
-3x^2 + 12x - 2x^2 - 6x
\][/tex]
4. Now, combine like terms:
[tex]\[
-3x^2 - 2x^2 = -5x^2
\][/tex]
[tex]\[
12x - 6x = 6x
\][/tex]
5. Therefore, the simplified expression is:
[tex]\[
-5x^2 + 6x
\][/tex]
Now, let's match this with the provided options:
1) [tex]\(-x^2 - 1\)[/tex]
2) [tex]\(-x^2 + 18x\)[/tex]
3) [tex]\(-5x^2 - 6x\)[/tex]
4) [tex]\(-5x^2 + 6x\)[/tex]
The expression that matches our simplified result [tex]\(-5x^2 + 6x\)[/tex] is:
[tex]\[ \boxed{-5x^2 + 6x} \][/tex]
Thus, the correct answer is option 4.
