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.
------------------------------------------------ Which of the following expressions is equivalent to [tex]-4x^3 - 12x^3 + 9x^2[/tex]?

A. [tex]x^8[/tex]
B. [tex]-7x^8[/tex]
C. [tex]-8x^3 + 9x^2[/tex]
D. [tex]-16x^3 + 9x^2[/tex]
E. [tex]-16x^6 + 9x^2[/tex]

Certainly! Let's simplify the given expression step-by-step.

We have the expression:

[tex]\[
-4x^3 - 12x^3 + 9x^2
\][/tex]

Step 1: Combine like terms.

First, look at the terms that involve [tex]\(x^3\)[/tex]:

- [tex]\(-4x^3\)[/tex]
- [tex]\(-12x^3\)[/tex]

To combine these, add the coefficients together:

- [tex]\(-4 - 12 = -16\)[/tex]

So, the combined [tex]\(x^3\)[/tex] terms become:

[tex]\[
-16x^3
\][/tex]

Step 2: Identify the remaining terms.

The only other term in the expression is:

- [tex]\(9x^2\)[/tex]

Step 3: Write the simplified expression.

Combine the results from Step 1 and the remaining term:

[tex]\[
-16x^3 + 9x^2
\][/tex]

Now, compare this simplified expression with the given options:

- A. [tex]\(x^8\)[/tex]
- B. [tex]\(-7x^8\)[/tex]
- C. [tex]\(-8x^3 + 9x^2\)[/tex]
- D. [tex]\(-16x^3 + 9x^2\)[/tex]
- E. [tex]\(-16x^6 + 9x^2\)[/tex]

The expression [tex]\(-16x^3 + 9x^2\)[/tex] matches option D.

Therefore, the correct choice is:

D. [tex]\(-16x^3 + 9x^2\)[/tex]