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.
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.
