Let's simplify the expression [tex]\(-3x^2(5x - 4x^2 - 6)\)[/tex] step by step:
1. Identify the terms inside the parentheses:
The terms inside the parentheses are [tex]\(5x\)[/tex], [tex]\(-4x^2\)[/tex], and [tex]\(-6\)[/tex].
2. Apply the distributive property:
This means we will multiply [tex]\(-3x^2\)[/tex] by each term inside the parentheses individually.
- First, we multiply [tex]\(-3x^2\)[/tex] by [tex]\(5x\)[/tex]:
[tex]\[
-3x^2 \cdot 5x = -15x^3
\][/tex]
- Next, we multiply [tex]\(-3x^2\)[/tex] by [tex]\(-4x^2\)[/tex]:
[tex]\[
-3x^2 \cdot -4x^2 = 12x^4
\][/tex]
Notice that the multiplication of two negative numbers results in a positive number.
- Finally, we multiply [tex]\(-3x^2\)[/tex] by [tex]\(-6\)[/tex]:
[tex]\[
-3x^2 \cdot -6 = 18x^2
\][/tex]
Again, the multiplication of two negative numbers results in a positive number.
3. Combine the results:
We now gather all the terms obtained from the distributive property:
[tex]\[
12x^4 - 15x^3 + 18x^2
\][/tex]
Therefore, the correct simplification of the expression [tex]\(-3x^2(5x - 4x^2 - 6)\)[/tex] is:
[tex]\[
\boxed{12x^4 - 15x^3 + 18x^2}
\][/tex]
