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.
[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.