Answer :
Certainly! Let's simplify the given expression step-by-step.
We have the expression:
[tex]\[
-4x^3 - 12x^3 + 9x^2
\][/tex]
Step 1: Combine like terms.
First, look at the terms that involve [tex]\(x^3\)[/tex]:
- [tex]\(-4x^3\)[/tex]
- [tex]\(-12x^3\)[/tex]
To combine these, add the coefficients together:
- [tex]\(-4 - 12 = -16\)[/tex]
So, the combined [tex]\(x^3\)[/tex] terms become:
[tex]\[
-16x^3
\][/tex]
Step 2: Identify the remaining terms.
The only other term in the expression is:
- [tex]\(9x^2\)[/tex]
Step 3: Write the simplified expression.
Combine the results from Step 1 and the remaining term:
[tex]\[
-16x^3 + 9x^2
\][/tex]
Now, compare this simplified expression with the given options:
- 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]
The expression [tex]\(-16x^3 + 9x^2\)[/tex] matches option D.
Therefore, the correct choice is:
D. [tex]\(-16x^3 + 9x^2\)[/tex]
We have the expression:
[tex]\[
-4x^3 - 12x^3 + 9x^2
\][/tex]
Step 1: Combine like terms.
First, look at the terms that involve [tex]\(x^3\)[/tex]:
- [tex]\(-4x^3\)[/tex]
- [tex]\(-12x^3\)[/tex]
To combine these, add the coefficients together:
- [tex]\(-4 - 12 = -16\)[/tex]
So, the combined [tex]\(x^3\)[/tex] terms become:
[tex]\[
-16x^3
\][/tex]
Step 2: Identify the remaining terms.
The only other term in the expression is:
- [tex]\(9x^2\)[/tex]
Step 3: Write the simplified expression.
Combine the results from Step 1 and the remaining term:
[tex]\[
-16x^3 + 9x^2
\][/tex]
Now, compare this simplified expression with the given options:
- 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]
The expression [tex]\(-16x^3 + 9x^2\)[/tex] matches option D.
Therefore, the correct choice is:
D. [tex]\(-16x^3 + 9x^2\)[/tex]
