Answer :
Let's simplify the expression step-by-step to find its equivalent:
We have the expression:
[tex]\[
-4x^3 - 12x^3 + 9x^2
\][/tex]
1. Combine Like Terms:
- The terms [tex]\(-4x^3\)[/tex] and [tex]\(-12x^3\)[/tex] both have [tex]\(x^3\)[/tex] as the variable part. We can combine these by adding their coefficients:
[tex]\[
-4x^3 - 12x^3 = (-4 - 12)x^3 = -16x^3
\][/tex]
2. Write the Simplified Expression:
- After combining the [tex]\(x^3\)[/tex] terms, we add the [tex]\(+9x^2\)[/tex] part, resulting in the simplified expression:
[tex]\[
-16x^3 + 9x^2
\][/tex]
Let's compare this with the given options:
- [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]
The simplified expression [tex]\(-16x^3 + 9x^2\)[/tex] matches the option:
[tex]\[
\boxed{-16x^3 + 9x^2}
\][/tex]
So, the expression [tex]\(-4x^3 - 12x^3 + 9x^2\)[/tex] is equivalent to [tex]\(-16x^3 + 9x^2\)[/tex].
We have the expression:
[tex]\[
-4x^3 - 12x^3 + 9x^2
\][/tex]
1. Combine Like Terms:
- The terms [tex]\(-4x^3\)[/tex] and [tex]\(-12x^3\)[/tex] both have [tex]\(x^3\)[/tex] as the variable part. We can combine these by adding their coefficients:
[tex]\[
-4x^3 - 12x^3 = (-4 - 12)x^3 = -16x^3
\][/tex]
2. Write the Simplified Expression:
- After combining the [tex]\(x^3\)[/tex] terms, we add the [tex]\(+9x^2\)[/tex] part, resulting in the simplified expression:
[tex]\[
-16x^3 + 9x^2
\][/tex]
Let's compare this with the given options:
- [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]
The simplified expression [tex]\(-16x^3 + 9x^2\)[/tex] matches the option:
[tex]\[
\boxed{-16x^3 + 9x^2}
\][/tex]
So, the expression [tex]\(-4x^3 - 12x^3 + 9x^2\)[/tex] is equivalent to [tex]\(-16x^3 + 9x^2\)[/tex].
