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Answer :
Let's simplify the given expression step-by-step:
The original expression is:
[tex]\[ -4x^3 - 12x^3 + 9x^2 \][/tex]
1. Combine like terms:
- Look at the terms with [tex]\(x^3\)[/tex]:
[tex]\[ -4x^3 - 12x^3 \][/tex]
Here, you can combine these because they both have the same variable part ([tex]\(x^3\)[/tex]):
[tex]\[ -4x^3 - 12x^3 = (-4 - 12)x^3 = -16x^3 \][/tex]
- Next, we have the [tex]\(x^2\)[/tex] term, which is:
[tex]\[ +9x^2 \][/tex]
There are no other terms with [tex]\(x^2\)[/tex] to combine with, so it stays the same.
2. Write the simplified expression:
Combine the results from steps above:
[tex]\[ -16x^3 + 9x^2 \][/tex]
So, the expression equivalent to [tex]\(-4x^3 - 12x^3 + 9x^2\)[/tex] is:
[tex]\[ -16x^3 + 9x^2 \][/tex]
Therefore, the correct choice is:
- [tex]\(-16x^3 + 9x^2\)[/tex]
The original expression is:
[tex]\[ -4x^3 - 12x^3 + 9x^2 \][/tex]
1. Combine like terms:
- Look at the terms with [tex]\(x^3\)[/tex]:
[tex]\[ -4x^3 - 12x^3 \][/tex]
Here, you can combine these because they both have the same variable part ([tex]\(x^3\)[/tex]):
[tex]\[ -4x^3 - 12x^3 = (-4 - 12)x^3 = -16x^3 \][/tex]
- Next, we have the [tex]\(x^2\)[/tex] term, which is:
[tex]\[ +9x^2 \][/tex]
There are no other terms with [tex]\(x^2\)[/tex] to combine with, so it stays the same.
2. Write the simplified expression:
Combine the results from steps above:
[tex]\[ -16x^3 + 9x^2 \][/tex]
So, the expression equivalent to [tex]\(-4x^3 - 12x^3 + 9x^2\)[/tex] is:
[tex]\[ -16x^3 + 9x^2 \][/tex]
Therefore, the correct choice is:
- [tex]\(-16x^3 + 9x^2\)[/tex]
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