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Which of the following expressions is equivalent to [tex]-4x^3 - 12x^3 + 9x^2[/tex]?

F. [tex]x^8[/tex]

G. [tex]-7x^8[/tex]

H. [tex]-8x^3 + 9x^2[/tex]

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

K. [tex]-16x^6 + 9x^2[/tex]

Answer :

Sure! Let's work through the problem step-by-step to find which expression is equivalent to [tex]\(-4x^3 - 12x^3 + 9x^2\)[/tex].

1. Identify and Combine Like Terms:

- Start with the expression: [tex]\(-4x^3 - 12x^3 + 9x^2\)[/tex].
- Notice that [tex]\(-4x^3\)[/tex] and [tex]\(-12x^3\)[/tex] are like terms because they both have [tex]\(x^3\)[/tex].
- Combine these terms:
[tex]\[
-4x^3 - 12x^3 = -16x^3
\][/tex]

2. Write the Simplified Expression:

- After combining like terms, the expression becomes:
[tex]\[
-16x^3 + 9x^2
\][/tex]

3. Look for the Matching Option:

- Check the given options:
- F. [tex]\(x^8\)[/tex]
- G. [tex]\(-7x^8\)[/tex]
- H. [tex]\(-8x^3 + 9x^2\)[/tex]
- J. [tex]\(-16x^3 + 9x^2\)[/tex]
- K. [tex]\(-16x^6 + 9x^2\)[/tex]

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

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

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