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

F. [tex]x^8[/tex]

G. [tex]-7x^8[/tex]

H. [tex]-8x^3 + 9x^2[/tex]

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

K. [tex]-16x^6 + 9x^2[/tex]

Sure! Let's work through the problem step-by-step to find which expression is equivalent to [tex]$-4x^3 - 12x^3 + 9x^2$[/tex].

1. Identify and Combine Like Terms:

- Start with the expression: [tex]$-4x^3 - 12x^3 + 9x^2$[/tex].
- Notice that [tex]$-4x^3$[/tex] and [tex]$-12x^3$[/tex] are like terms because they both have [tex]$x^3$[/tex].
- Combine these terms:
[tex]\[
-4x^3 - 12x^3 = -16x^3
\][/tex]

2. Write the Simplified Expression:

- After combining like terms, the expression becomes:
[tex]\[
-16x^3 + 9x^2
\][/tex]

3. Look for the Matching Option:

- Check the given options:
- F. [tex]$x^8$[/tex]
- G. [tex]$-7x^8$[/tex]
- H. [tex]$-8x^3 + 9x^2$[/tex]
- J. [tex]$-16x^3 + 9x^2$[/tex]
- K. [tex]$-16x^6 + 9x^2$[/tex]

- The simplified expression [tex]$-16x^3 + 9x^2$[/tex] matches option J.

So, the correct answer is J: [tex]$-16x^3 + 9x^2$[/tex].