Answer :
To simplify the expression [tex]\(-4 x^2\left(6 x - 5 x^2 - 5\right)\)[/tex], follow these steps:
1. Distribute the [tex]\(-4x^2\)[/tex] into each term inside the parentheses:
- Multiply [tex]\(-4x^2\)[/tex] by [tex]\(6x\)[/tex]:
[tex]\[
-4x^2 \times 6x = -24x^3
\][/tex]
- Multiply [tex]\(-4x^2\)[/tex] by [tex]\(-5x^2\)[/tex]:
[tex]\[
-4x^2 \times -5x^2 = 20x^4
\][/tex]
- Multiply [tex]\(-4x^2\)[/tex] by [tex]\(-5\)[/tex]:
[tex]\[
-4x^2 \times -5 = 20x^2
\][/tex]
2. Combine all the terms:
The expression can now be written as:
[tex]\[
20x^4 - 24x^3 + 20x^2
\][/tex]
Thus, the simplified form of the expression is [tex]\(20x^4 - 24x^3 + 20x^2\)[/tex].
This matches the choice:
[tex]\[ \boxed{20 x^4 - 24 x^3 + 20 x^2} \][/tex]
1. Distribute the [tex]\(-4x^2\)[/tex] into each term inside the parentheses:
- Multiply [tex]\(-4x^2\)[/tex] by [tex]\(6x\)[/tex]:
[tex]\[
-4x^2 \times 6x = -24x^3
\][/tex]
- Multiply [tex]\(-4x^2\)[/tex] by [tex]\(-5x^2\)[/tex]:
[tex]\[
-4x^2 \times -5x^2 = 20x^4
\][/tex]
- Multiply [tex]\(-4x^2\)[/tex] by [tex]\(-5\)[/tex]:
[tex]\[
-4x^2 \times -5 = 20x^2
\][/tex]
2. Combine all the terms:
The expression can now be written as:
[tex]\[
20x^4 - 24x^3 + 20x^2
\][/tex]
Thus, the simplified form of the expression is [tex]\(20x^4 - 24x^3 + 20x^2\)[/tex].
This matches the choice:
[tex]\[ \boxed{20 x^4 - 24 x^3 + 20 x^2} \][/tex]
