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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 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].

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