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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 :

Sure, let's simplify the expression step by step.

We have the expression: [tex]\(-4x^3 - 12x^3 + 9x^2\)[/tex].

1. Combine like terms for [tex]\(x^3\)[/tex]:

The terms [tex]\(-4x^3\)[/tex] and [tex]\(-12x^3\)[/tex] are like terms because they both contain [tex]\(x^3\)[/tex]. We can add them together:

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

2. Write the full simplified expression:

After combining the like terms, we add the [tex]\(9x^2\)[/tex] term:

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

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

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

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