Answer :
To solve the problem and find which expression is equivalent to [tex]\(-4x^3 - 12x^3 + 9x^2\)[/tex], follow these steps:
1. Identify the Terms:
- The expression is made up of two types of terms: those involving [tex]\(x^3\)[/tex] and those involving [tex]\(x^2\)[/tex].
2. Combine Like Terms:
- Look at the [tex]\(x^3\)[/tex] terms: [tex]\(-4x^3\)[/tex] and [tex]\(-12x^3\)[/tex].
- These terms share the same variable and exponent, so you can add their coefficients: [tex]\(-4 + (-12) = -16\)[/tex].
- This gives us [tex]\(-16x^3\)[/tex].
3. Write the Simplified Expression:
- Combine the results to rewrite the entire expression:
[tex]\[
-16x^3 + 9x^2
\][/tex]
4. Choose the Equivalent Expression:
- From the list of 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 simplified expression from our calculations is [tex]\(-16x^3 + 9x^2\)[/tex].
Therefore, the expression that is equivalent to the original one is [tex]\(-16x^3 + 9x^2\)[/tex].
1. Identify the Terms:
- The expression is made up of two types of terms: those involving [tex]\(x^3\)[/tex] and those involving [tex]\(x^2\)[/tex].
2. Combine Like Terms:
- Look at the [tex]\(x^3\)[/tex] terms: [tex]\(-4x^3\)[/tex] and [tex]\(-12x^3\)[/tex].
- These terms share the same variable and exponent, so you can add their coefficients: [tex]\(-4 + (-12) = -16\)[/tex].
- This gives us [tex]\(-16x^3\)[/tex].
3. Write the Simplified Expression:
- Combine the results to rewrite the entire expression:
[tex]\[
-16x^3 + 9x^2
\][/tex]
4. Choose the Equivalent Expression:
- From the list of 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 simplified expression from our calculations is [tex]\(-16x^3 + 9x^2\)[/tex].
Therefore, the expression that is equivalent to the original one is [tex]\(-16x^3 + 9x^2\)[/tex].
