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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]

Answer :

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.