Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Choose the correct simplification of the expression [tex]-4x^2(6x-5x^2-5)[/tex].

A. [tex]20x^4 + 24x^3 + 20x^2[/tex]

B. [tex]-9x^4 + 2x^3 - 9x^2[/tex]

C. [tex]20x^4 - 24x^3 + 20x^2[/tex]

D. [tex]-20x^4 + 24x^3 - 20x^2[/tex]

Sure! Let's simplify the expression step-by-step:

We are given the expression:
[tex]\[
-4x^2(6x - 5x^2 - 5)
\][/tex]

We need to distribute [tex]$-4x^2$[/tex] across each term inside the parentheses:

1. Distribute [tex]$-4x^2$[/tex] to [tex]$6x$[/tex]:
[tex]\[
-4x^2 \cdot 6x = -24x^3
\][/tex]

2. Distribute [tex]$-4x^2$[/tex] to [tex]$-5x^2$[/tex]:
[tex]\[
-4x^2 \cdot (-5x^2) = 20x^4
\][/tex]

3. Distribute [tex]$-4x^2$[/tex] to [tex]$-5$[/tex]:
[tex]\[
-4x^2 \cdot (-5) = 20x^2
\][/tex]

Now, let's combine all these results to write the simplified expression:
[tex]\[
20x^4 - 24x^3 + 20x^2
\][/tex]

Therefore, the correct simplification of the expression [tex]$-4x^2(6x - 5x^2 - 5)$[/tex] is:
[tex]\[
20x^4 - 24x^3 + 20x^2
\][/tex]

So, the correct choice from the given options is [tex]$20x^4 - 24x^3 + 20x^2$[/tex].