High School

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

F. [tex]x^3[/tex]

G. [tex]-7x^3[/tex]

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

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

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

Answer :

Certainly! Let's solve the expression step-by-step:

We are given the expression:
[tex]\[
-4x^3 - 12x^3 + 9x^2
\][/tex]

Step 1: Combine like terms.

- The expression has terms that are similar: [tex]\(-4x^3\)[/tex] and [tex]\(-12x^3\)[/tex].
- Combine these terms by adding their coefficients:
[tex]\[
-4x^3 - 12x^3 = (-4 - 12)x^3 = -16x^3
\][/tex]

Step 2: Write the expression with the combined terms.

- After combining, the expression becomes:
[tex]\[
-16x^3 + 9x^2
\][/tex]

So, the expression [tex]\(-4x^3 - 12x^3 + 9x^2\)[/tex] simplifies to [tex]\(-16x^3 + 9x^2\)[/tex].

Therefore, the expression that is equivalent to the given one is:

J. [tex]\(-16x^3 + 9x^2\)[/tex]

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