High School

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 :

We start with the expression

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

Step 1: Combine like terms for the [tex]$x^3$[/tex] terms.

The [tex]$x^3$[/tex] terms are [tex]$-4x^3$[/tex] and [tex]$-12x^3$[/tex]. Adding the coefficients gives:

[tex]$$
-4 + (-12) = -16.
$$[/tex]

So, the combined [tex]$x^3$[/tex] term is:

[tex]$$
-16x^3.
$$[/tex]

Step 2: Retain the [tex]$x^2$[/tex] term.

The [tex]$x^2$[/tex] term is [tex]$9x^2$[/tex], which remains unchanged.

Step 3: Write the simplified expression.

The expression becomes:

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

Step 4: Identify the matching option.

Among the choices provided, the expression that matches the simplified form is:

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

This corresponds to option D.

Therefore, the correct answer is D.

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