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]

We start with the expression

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

Step 1: Combine like terms for the [tex]$x^3$[/tex] terms.

The [tex]$x^3$[/tex] terms are [tex]$-4x^3$[/tex] and [tex]$-12x^3$[/tex]. Adding the coefficients gives:

[tex]$$
-4 + (-12) = -16.
$$[/tex]

So, the combined [tex]$x^3$[/tex] term is:

[tex]$$
-16x^3.
$$[/tex]

Step 2: Retain the [tex]$x^2$[/tex] term.

The [tex]$x^2$[/tex] term is [tex]$9x^2$[/tex], which remains unchanged.

Step 3: Write the simplified expression.

The expression becomes:

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

Step 4: Identify the matching option.

Among the choices provided, the expression that matches the simplified form is:

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

This corresponds to option D.

Therefore, the correct answer is D.