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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 :

Certainly! Let's simplify the given expression step-by-step.

We have the expression:

[tex]\[
-4x^3 - 12x^3 + 9x^2
\][/tex]

Step 1: Combine like terms.

First, look at the terms that involve [tex]\(x^3\)[/tex]:

- [tex]\(-4x^3\)[/tex]
- [tex]\(-12x^3\)[/tex]

To combine these, add the coefficients together:

- [tex]\(-4 - 12 = -16\)[/tex]

So, the combined [tex]\(x^3\)[/tex] terms become:

[tex]\[
-16x^3
\][/tex]

Step 2: Identify the remaining terms.

The only other term in the expression is:

- [tex]\(9x^2\)[/tex]

Step 3: Write the simplified expression.

Combine the results from Step 1 and the remaining term:

[tex]\[
-16x^3 + 9x^2
\][/tex]

Now, compare this simplified expression with the given options:

- 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]

The expression [tex]\(-16x^3 + 9x^2\)[/tex] matches option D.

Therefore, the correct choice is:

D. [tex]\(-16x^3 + 9x^2\)[/tex]

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