High School

Which of the following expressions is equivalent to [tex]-4x^3 - 12x^3 + 9x^2[/tex]?

A. [tex]x^8[/tex]

B. [tex]-7x^8[/tex]

C. [tex]-8x^3 + 9x^2[/tex]

D. [tex]-16x^3 + 9x^2[/tex]

E. [tex]-16x^6 + 9x^2[/tex]

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].