To simplify the expression [tex]\(-5 x^2 (4x - 6x^2 - 3)\)[/tex], we need to distribute [tex]\(-5 x^2\)[/tex] to each term inside the parentheses. Let's break it down step by step:
1. Start with the expression:
[tex]\[
-5 x^2 (4x - 6x^2 - 3)
\][/tex]
2. Distribute [tex]\(-5 x^2\)[/tex] to each term inside the parentheses:
[tex]\[
= (-5 x^2) \cdot (4x) + (-5 x^2) \cdot (-6x^2) + (-5 x^2) \cdot (-3)
\][/tex]
3. Multiply each term:
[tex]\[
(-5 x^2) \cdot (4x) = -20 x^3
\][/tex]
[tex]\[
(-5 x^2) \cdot (-6x^2) = 30 x^4
\][/tex]
[tex]\[
(-5 x^2) \cdot (-3) = 15 x^2
\][/tex]
4. Combine all the terms:
[tex]\[
30 x^4 - 20 x^3 + 15 x^2
\][/tex]
So, the simplified expression is:
[tex]\[
30 x^4 - 20 x^3 + 15 x^2
\][/tex]
This matches the first option given. Therefore, the correct simplification is:
[tex]\[
\boxed{30 x^4 - 20 x^3 + 15 x^2}
\][/tex]
