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Answer :
To solve the problem of finding an equivalent expression to [tex]\(-4x^3 - 12x^3 + 9x^2\)[/tex], follow these steps:
1. Identify and Combine Like Terms:
- Look for terms that have the same variable raised to the same power. In this case, the terms [tex]\(-4x^3\)[/tex] and [tex]\(-12x^3\)[/tex] have the same variable part [tex]\(x^3\)[/tex].
- Combine these terms by adding their coefficients:
[tex]\[
-4x^3 - 12x^3 = (-4 - 12)x^3 = -16x^3
\][/tex]
2. Write the Simplified Expression:
- After combining the like terms, you should now have:
[tex]\[
-16x^3 + 9x^2
\][/tex]
- The term [tex]\(9x^2\)[/tex] remains as is because it does not have a like term to combine with.
3. Check the Given Options:
- Now, compare the simplified expression [tex]\(-16x^3 + 9x^2\)[/tex] 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]
4. Select the Equivalent Expression:
- The expression that matches our simplified form is [tex]\(-16x^3 + 9x^2\)[/tex].
Therefore, the equivalent expression to [tex]\(-4x^3 - 12x^3 + 9x^2\)[/tex] is [tex]\(-16x^3 + 9x^2\)[/tex].
1. Identify and Combine Like Terms:
- Look for terms that have the same variable raised to the same power. In this case, the terms [tex]\(-4x^3\)[/tex] and [tex]\(-12x^3\)[/tex] have the same variable part [tex]\(x^3\)[/tex].
- Combine these terms by adding their coefficients:
[tex]\[
-4x^3 - 12x^3 = (-4 - 12)x^3 = -16x^3
\][/tex]
2. Write the Simplified Expression:
- After combining the like terms, you should now have:
[tex]\[
-16x^3 + 9x^2
\][/tex]
- The term [tex]\(9x^2\)[/tex] remains as is because it does not have a like term to combine with.
3. Check the Given Options:
- Now, compare the simplified expression [tex]\(-16x^3 + 9x^2\)[/tex] 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]
4. Select the Equivalent Expression:
- The expression that matches our simplified form is [tex]\(-16x^3 + 9x^2\)[/tex].
Therefore, the equivalent expression to [tex]\(-4x^3 - 12x^3 + 9x^2\)[/tex] is [tex]\(-16x^3 + 9x^2\)[/tex].
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