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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 given in the question: [tex]\(-4x^3 - 12x^3 + 9x^2\)[/tex].

### Step 1: Combine Like Terms
- The like terms in the expression are [tex]\(-4x^3\)[/tex] and [tex]\(-12x^3\)[/tex]. We can combine these by adding their coefficients:
[tex]\[
-4x^3 - 12x^3 = (-4 - 12)x^3 = -16x^3
\][/tex]

- The term [tex]\(9x^2\)[/tex] does not have a like term to combine with, so it remains the same.

### Step 2: Write the Simplified Expression
- Combining the results from step 1, we have:
[tex]\[
-16x^3 + 9x^2
\][/tex]

Now, let's compare this to the given options to find the equivalent expression:

1. [tex]\(x^8\)[/tex]
2. [tex]\(-7x^8\)[/tex]
3. [tex]\(-8x^3 + 9x^2\)[/tex]
4. [tex]\(-16x^3 + 9x^2\)[/tex]
5. [tex]\(-16x^6 + 9x^2\)[/tex]

The option that matches the simplified expression [tex]\(-16x^3 + 9x^2\)[/tex] is:

Option 4: [tex]\(-16x^3 + 9x^2\)[/tex]

Therefore, the answer is [tex]\(-16x^3 + 9x^2\)[/tex].

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