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Answer :
To solve the problem and determine which of the given expressions is equivalent to [tex]\(-4x^3 - 12x^3 + 9x^2\)[/tex], let's break it down step-by-step:
1. Combine Like Terms:
- First, notice that both [tex]\(-4x^3\)[/tex] and [tex]\(-12x^3\)[/tex] have the same variable part, which is [tex]\(x^3\)[/tex]. Therefore, they are like terms and can be combined.
- Add the coefficients of these terms: [tex]\(-4\)[/tex] and [tex]\(-12\)[/tex].
[tex]\[
-4x^3 - 12x^3 = (-4 - 12)x^3 = -16x^3
\][/tex]
2. Reconstruct the Expression:
- After combining the like terms, you still have the term [tex]\(9x^2\)[/tex] from the original expression.
- Therefore, the expression becomes:
[tex]\[
-16x^3 + 9x^2
\][/tex]
3. Select the Equivalent Expression:
- Now, compare this simplified expression with the options provided:
- [tex]\(x^8\)[/tex]
- [tex]\(-7x^8\)[/tex]
- [tex]\(-8x^3 + 9x^2\)[/tex]
- [tex]\(-16x^3 + 9x^2\)[/tex]
- [tex]\(-16x^6 + 9x^2\)[/tex]
- The expression [tex]\(-16x^3 + 9x^2\)[/tex] matches exactly with one of the options: [tex]\(-16x^3 + 9x^2\)[/tex].
Thus, the expression equivalent to [tex]\(-4x^3 - 12x^3 + 9x^2\)[/tex] is [tex]\(-16x^3 + 9x^2\)[/tex].
1. Combine Like Terms:
- First, notice that both [tex]\(-4x^3\)[/tex] and [tex]\(-12x^3\)[/tex] have the same variable part, which is [tex]\(x^3\)[/tex]. Therefore, they are like terms and can be combined.
- Add the coefficients of these terms: [tex]\(-4\)[/tex] and [tex]\(-12\)[/tex].
[tex]\[
-4x^3 - 12x^3 = (-4 - 12)x^3 = -16x^3
\][/tex]
2. Reconstruct the Expression:
- After combining the like terms, you still have the term [tex]\(9x^2\)[/tex] from the original expression.
- Therefore, the expression becomes:
[tex]\[
-16x^3 + 9x^2
\][/tex]
3. Select the Equivalent Expression:
- Now, compare this simplified expression with the options provided:
- [tex]\(x^8\)[/tex]
- [tex]\(-7x^8\)[/tex]
- [tex]\(-8x^3 + 9x^2\)[/tex]
- [tex]\(-16x^3 + 9x^2\)[/tex]
- [tex]\(-16x^6 + 9x^2\)[/tex]
- The expression [tex]\(-16x^3 + 9x^2\)[/tex] matches exactly with one of the options: [tex]\(-16x^3 + 9x^2\)[/tex].
Thus, the expression equivalent to [tex]\(-4x^3 - 12x^3 + 9x^2\)[/tex] is [tex]\(-16x^3 + 9x^2\)[/tex].
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