To simplify the expression [tex]\(-5 x^2(4 x - 6 x^2 - 3)\)[/tex], we'll take it step by step by distributing [tex]\(-5 x^2\)[/tex] to each term inside the parentheses:
Given expression:
[tex]\[
-5 x^2 (4 x - 6 x^2 - 3)
\][/tex]
Step 1: Distribute [tex]\(-5 x^2\)[/tex] to [tex]\(4 x\)[/tex]:
[tex]\[
-5 x^2 \cdot 4 x = -20 x^3
\][/tex]
Step 2: Distribute [tex]\(-5 x^2\)[/tex] to [tex]\(-6 x^2\)[/tex]:
[tex]\[
-5 x^2 \cdot (-6 x^2) = 30 x^4
\][/tex]
Step 3: Distribute [tex]\(-5 x^2\)[/tex] to [tex]\(-3\)[/tex]:
[tex]\[
-5 x^2 \cdot (-3) = 15 x^2
\][/tex]
Now we combine all these results:
[tex]\[
30 x^4 - 20 x^3 + 15 x^2
\][/tex]
Hence, the correct simplification of the expression [tex]\(-5 x^2(4 x - 6 x^2 - 3)\)[/tex] is:
[tex]\[
-30 x^4 + 20 x^3 - 15 x^2
\][/tex]
Therefore, the correct choice is:
[tex]\[
\boxed{-30 x^4 + 20 x^3 - 15 x^2}
\][/tex]
