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Answer :
To find the expression that is equivalent to [tex]\(-4x^3 - 12x^3 + 9x^2\)[/tex], follow these steps:
1. Combine Like Terms: Look for terms with the same variable and the same exponent. In our expression, we have:
- Two terms with [tex]\(x^3\)[/tex]: [tex]\(-4x^3\)[/tex] and [tex]\(-12x^3\)[/tex].
- One term with [tex]\(x^2\)[/tex]: [tex]\(9x^2\)[/tex].
2. Add the Coefficients for Like Terms:
- For the [tex]\(x^3\)[/tex] terms: [tex]\(-4x^3 - 12x^3\)[/tex] combines to [tex]\((-4 - 12)x^3 = -16x^3\)[/tex].
3. Write the Simplified Expression: Combine the simplified [tex]\(x^3\)[/tex] term with the [tex]\(x^2\)[/tex] term:
- This gives us [tex]\(-16x^3 + 9x^2\)[/tex].
So, the expression that is equivalent to [tex]\(-4x^3 - 12x^3 + 9x^2\)[/tex] is [tex]\(-16x^3 + 9x^2\)[/tex].
Therefore, the correct choice from the given options is [tex]\(-16x^3 + 9x^2\)[/tex].
1. Combine Like Terms: Look for terms with the same variable and the same exponent. In our expression, we have:
- Two terms with [tex]\(x^3\)[/tex]: [tex]\(-4x^3\)[/tex] and [tex]\(-12x^3\)[/tex].
- One term with [tex]\(x^2\)[/tex]: [tex]\(9x^2\)[/tex].
2. Add the Coefficients for Like Terms:
- For the [tex]\(x^3\)[/tex] terms: [tex]\(-4x^3 - 12x^3\)[/tex] combines to [tex]\((-4 - 12)x^3 = -16x^3\)[/tex].
3. Write the Simplified Expression: Combine the simplified [tex]\(x^3\)[/tex] term with the [tex]\(x^2\)[/tex] term:
- This gives us [tex]\(-16x^3 + 9x^2\)[/tex].
So, the expression that is equivalent to [tex]\(-4x^3 - 12x^3 + 9x^2\)[/tex] is [tex]\(-16x^3 + 9x^2\)[/tex].
Therefore, the correct choice from the given options is [tex]\(-16x^3 + 9x^2\)[/tex].
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