Answer :
Sure, let's simplify the expression step by step:
The expression given is [tex]\(-4 x^2(6 x - 5 x^2 - 5)\)[/tex].
Step 1: Distribute [tex]\(-4 x^2\)[/tex] into the expression inside the parentheses.
1. Multiply [tex]\(-4 x^2\)[/tex] with [tex]\(6 x\)[/tex]:
[tex]\[
-4 x^2 \cdot 6 x = -24 x^3
\][/tex]
2. Multiply [tex]\(-4 x^2\)[/tex] with [tex]\(-5 x^2\)[/tex]:
[tex]\[
-4 x^2 \cdot (-5 x^2) = 20 x^4
\][/tex]
3. Multiply [tex]\(-4 x^2\)[/tex] with [tex]\(-5\)[/tex]:
[tex]\[
-4 x^2 \cdot (-5) = 20 x^2
\][/tex]
Step 2: Combine all the terms.
Now, put all these products together:
[tex]\[
20 x^4 - 24 x^3 + 20 x^2
\][/tex]
Step 3: Match with the given options.
The correctly simplified expression matches the third option:
[tex]\[
20 x^4 - 24 x^3 + 20 x^2
\][/tex]
So, the correct answer is:
[tex]\[
20 x^4 - 24 x^3 + 20 x^2
\][/tex]
The expression given is [tex]\(-4 x^2(6 x - 5 x^2 - 5)\)[/tex].
Step 1: Distribute [tex]\(-4 x^2\)[/tex] into the expression inside the parentheses.
1. Multiply [tex]\(-4 x^2\)[/tex] with [tex]\(6 x\)[/tex]:
[tex]\[
-4 x^2 \cdot 6 x = -24 x^3
\][/tex]
2. Multiply [tex]\(-4 x^2\)[/tex] with [tex]\(-5 x^2\)[/tex]:
[tex]\[
-4 x^2 \cdot (-5 x^2) = 20 x^4
\][/tex]
3. Multiply [tex]\(-4 x^2\)[/tex] with [tex]\(-5\)[/tex]:
[tex]\[
-4 x^2 \cdot (-5) = 20 x^2
\][/tex]
Step 2: Combine all the terms.
Now, put all these products together:
[tex]\[
20 x^4 - 24 x^3 + 20 x^2
\][/tex]
Step 3: Match with the given options.
The correctly simplified expression matches the third option:
[tex]\[
20 x^4 - 24 x^3 + 20 x^2
\][/tex]
So, the correct answer is:
[tex]\[
20 x^4 - 24 x^3 + 20 x^2
\][/tex]
