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------------------------------------------------ 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]

To find an expression equivalent to [tex]$-4x^3 - 12x^3 + 9x^2$[/tex], follow these steps:

1. Identify Like Terms: In the expression [tex]$-4x^3 - 12x^3 + 9x^2$[/tex], the terms [tex]$-4x^3$[/tex] and [tex]$-12x^3$[/tex] are like terms because they both contain [tex]$x^3$[/tex]. The term [tex]$9x^2$[/tex] is different because it involves [tex]$x^2$[/tex].

2. Combine Like Terms:
- Add the coefficients of the like terms [tex]$x^3$[/tex]. The coefficients are [tex]$-4$[/tex] and [tex]$-12$[/tex].
- Calculate [tex]$-4 + (-12) = -16$[/tex].

3. Write the Combined Expression:
- The combined expression for the [tex]$x^3$[/tex] terms is [tex]$-16x^3$[/tex].
- Since the term [tex]$9x^2$[/tex] does not have a like term to combine with, it remains as is.

4. Final Expression:
- The resulting expression is [tex]$-16x^3 + 9x^2$[/tex].

This corresponds to one of the given choices:
- [tex]$-16x^3 + 9x^2$[/tex]

Therefore, the expression equivalent to [tex]$-4x^3 - 12x^3 + 9x^2$[/tex] is [tex]$-16x^3 + 9x^2$[/tex].