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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 find the expression equivalent to [tex]\(-4x^3 - 12x^3 + 9x^2\)[/tex], we'll simplify it step by step.

1. Combine like terms:
The terms [tex]\(-4x^3\)[/tex] and [tex]\(-12x^3\)[/tex] are like terms because they both contain [tex]\(x^3\)[/tex].

[tex]\(-4x^3 - 12x^3\)[/tex] becomes [tex]\((-4 - 12)x^3 = -16x^3\)[/tex].

2. Write down the simplified expression:
After combining the like terms, we have the expression:
[tex]\(-16x^3 + 9x^2\)[/tex].

3. Compare 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 expression [tex]\(-16x^3 + 9x^2\)[/tex] exactly matches the fourth option.

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

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