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Answer :
To find an expression equivalent to [tex]\(-4x^3 - 12x^3 + 9x^2\)[/tex], follow these steps:
1. Identify Like Terms: In the expression [tex]\(-4x^3 - 12x^3 + 9x^2\)[/tex], the terms [tex]\(-4x^3\)[/tex] and [tex]\(-12x^3\)[/tex] are like terms because they both contain [tex]\(x^3\)[/tex]. The term [tex]\(9x^2\)[/tex] is different because it involves [tex]\(x^2\)[/tex].
2. Combine Like Terms:
- Add the coefficients of the like terms [tex]\(x^3\)[/tex]. The coefficients are [tex]\(-4\)[/tex] and [tex]\(-12\)[/tex].
- Calculate [tex]\(-4 + (-12) = -16\)[/tex].
3. Write the Combined Expression:
- The combined expression for the [tex]\(x^3\)[/tex] terms is [tex]\(-16x^3\)[/tex].
- Since the term [tex]\(9x^2\)[/tex] does not have a like term to combine with, it remains as is.
4. Final Expression:
- The resulting expression is [tex]\(-16x^3 + 9x^2\)[/tex].
This corresponds to one of the given choices:
- [tex]\(-16x^3 + 9x^2\)[/tex]
Therefore, the expression equivalent to [tex]\(-4x^3 - 12x^3 + 9x^2\)[/tex] is [tex]\(-16x^3 + 9x^2\)[/tex].
1. Identify Like Terms: In the expression [tex]\(-4x^3 - 12x^3 + 9x^2\)[/tex], the terms [tex]\(-4x^3\)[/tex] and [tex]\(-12x^3\)[/tex] are like terms because they both contain [tex]\(x^3\)[/tex]. The term [tex]\(9x^2\)[/tex] is different because it involves [tex]\(x^2\)[/tex].
2. Combine Like Terms:
- Add the coefficients of the like terms [tex]\(x^3\)[/tex]. The coefficients are [tex]\(-4\)[/tex] and [tex]\(-12\)[/tex].
- Calculate [tex]\(-4 + (-12) = -16\)[/tex].
3. Write the Combined Expression:
- The combined expression for the [tex]\(x^3\)[/tex] terms is [tex]\(-16x^3\)[/tex].
- Since the term [tex]\(9x^2\)[/tex] does not have a like term to combine with, it remains as is.
4. Final Expression:
- The resulting expression is [tex]\(-16x^3 + 9x^2\)[/tex].
This corresponds to one of the given choices:
- [tex]\(-16x^3 + 9x^2\)[/tex]
Therefore, the expression equivalent to [tex]\(-4x^3 - 12x^3 + 9x^2\)[/tex] is [tex]\(-16x^3 + 9x^2\)[/tex].
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