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]

Let's simplify the expression [tex]$-4x^3 - 12x^3 + 9x^2$[/tex] step-by-step to find an equivalent expression.

1. Identify Like Terms:
The expression includes like terms that we can combine. The terms [tex]$-4x^3$[/tex] and [tex]$-12x^3$[/tex] are both cubic terms (terms with [tex]$x^3$[/tex]).

2. Combine the Like Terms:
Add [tex]$-4x^3$[/tex] and [tex]$-12x^3$[/tex] together:
[tex]\[
-4x^3 - 12x^3 = -16x^3
\][/tex]

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

4. Conclusion:
The simplified expression is [tex]$-16x^3 + 9x^2$[/tex].

Therefore, the equivalent expression is [tex]$-16 x^3 + 9 x^2$[/tex]. This matches the choice [tex]$-16 x^3 + 9 x^2$[/tex] from the options provided.