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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 solve the problem of finding an equivalent expression to [tex]$-4x^3 - 12x^3 + 9x^2$[/tex], follow these steps:

1. Identify and Combine Like Terms:
- Look for terms that have the same variable raised to the same power. In this case, the terms [tex]$-4x^3$[/tex] and [tex]$-12x^3$[/tex] have the same variable part [tex]$x^3$[/tex].
- Combine these terms by adding their coefficients:
[tex]\[
-4x^3 - 12x^3 = (-4 - 12)x^3 = -16x^3
\][/tex]

2. Write the Simplified Expression:
- After combining the like terms, you should now have:
[tex]\[
-16x^3 + 9x^2
\][/tex]
- The term [tex]$9x^2$[/tex] remains as is because it does not have a like term to combine with.

3. Check the Given Options:
- Now, compare the simplified expression [tex]$-16x^3 + 9x^2$[/tex] with the options provided:
- [tex]$x^8$[/tex]
- [tex]$-7x^8$[/tex]
- [tex]$-8x^3 + 9x^2$[/tex]
- [tex]$-16x^3 + 9x^2$[/tex]
- [tex]$-16x^6 + 9x^2$[/tex]

4. Select the Equivalent Expression:
- The expression that matches our simplified form is [tex]$-16x^3 + 9x^2$[/tex].

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