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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 simplify the expression [tex]$-4 x^3 - 12 x^3 + 9 x^2$[/tex], follow these steps:

1. Identify like terms:
- We have two terms involving [tex]$x^3$[/tex] which are [tex]$-4 x^3$[/tex] and [tex]$-12 x^3$[/tex].
- We have one term involving [tex]$x^2$[/tex] which is [tex]$9 x^2$[/tex].

2. Combine like terms:
- For the [tex]$x^3$[/tex] terms: [tex]$-4 x^3 - 12 x^3 = -16 x^3$[/tex].
- The [tex]$x^2$[/tex] term [tex]$9 x^2$[/tex] remains as it is because there are no other [tex]$x^2$[/tex] terms to combine with.

3. Write the final simplified expression:
- Combining the results, the expression simplifies to [tex]$-16 x^3 + 9 x^2$[/tex].

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