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Answer :
To solve the problem, we need to simplify and combine like terms in the given expression: [tex]\(-4x^3 - 12x^3 + 9x^2\)[/tex].
Here's how to do it step by step:
1. Identify and Combine Like Terms:
- We have two terms with [tex]\(x^3\)[/tex]: [tex]\(-4x^3\)[/tex] and [tex]\(-12x^3\)[/tex].
- Combine these terms:
[tex]\[
-4x^3 - 12x^3 = -16x^3
\][/tex]
- The [tex]\(x^2\)[/tex] term remains as it is because there are no other [tex]\(x^2\)[/tex] terms to combine it with.
2. Write the Simplified Expression:
- After combining the like terms, the expression becomes:
[tex]\[
-16x^3 + 9x^2
\][/tex]
3. Match with the Choices Provided:
- We compare the simplified expression [tex]\(-16x^3 + 9x^2\)[/tex] with the given options:
- [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 that matches our simplified result is:
[tex]\(-16x^3 + 9x^2\)[/tex]
Therefore, the expression [tex]\(-16x^3 + 9x^2\)[/tex] is the correct equivalent expression for the given problem.
Here's how to do it step by step:
1. Identify and Combine Like Terms:
- We have two terms with [tex]\(x^3\)[/tex]: [tex]\(-4x^3\)[/tex] and [tex]\(-12x^3\)[/tex].
- Combine these terms:
[tex]\[
-4x^3 - 12x^3 = -16x^3
\][/tex]
- The [tex]\(x^2\)[/tex] term remains as it is because there are no other [tex]\(x^2\)[/tex] terms to combine it with.
2. Write the Simplified Expression:
- After combining the like terms, the expression becomes:
[tex]\[
-16x^3 + 9x^2
\][/tex]
3. Match with the Choices Provided:
- We compare the simplified expression [tex]\(-16x^3 + 9x^2\)[/tex] with the given options:
- [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 that matches our simplified result is:
[tex]\(-16x^3 + 9x^2\)[/tex]
Therefore, the expression [tex]\(-16x^3 + 9x^2\)[/tex] is the correct equivalent expression for the given problem.
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