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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 :

To solve the given expression and find the equivalent one, we will simplify by combining like terms. Here’s a step-by-step approach:

1. Identify the Terms:
The expression we need to simplify is [tex]\(-4x^3 - 12x^3 + 9x^2\)[/tex].

2. Combine Like Terms:
- The terms [tex]\(-4x^3\)[/tex] and [tex]\(-12x^3\)[/tex] are like terms because they both have [tex]\(x^3\)[/tex].
- Combine these terms by adding their coefficients: [tex]\(-4 - 12\)[/tex].
- This results in [tex]\(-16x^3\)[/tex].

3. Rewrite the Expression:
- After combining the like terms, you include the remaining term [tex]\(9x^2\)[/tex].
- So the simplified expression becomes [tex]\(-16x^3 + 9x^2\)[/tex].

4. Choose the Equivalent Expression:
- Compare the simplified expression [tex]\(-16x^3 + 9x^2\)[/tex] to the given options to find the match:
- Option 1: [tex]\(x^8\)[/tex]
- Option 2: [tex]\(-7x^8\)[/tex]
- Option 3: [tex]\(-8x^3 + 9x^2\)[/tex]
- Option 4: [tex]\(-16x^3 + 9x^2\)[/tex]
- Option 5: [tex]\(-16x^6 + 9x^2\)[/tex]

- The expression [tex]\(-16x^3 + 9x^2\)[/tex] matches Option 4 exactly.

Hence, the expression equivalent to [tex]\(-4x^3 - 12x^3 + 9x^2\)[/tex] is [tex]\(-16x^3 + 9x^2\)[/tex].

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