College

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 find the expression that is equivalent to [tex]\(-4x^3 - 12x^3 + 9x^2\)[/tex], follow these steps:

1. Combine Like Terms: Look for terms with the same variable and the same exponent. In our expression, we have:
- Two terms with [tex]\(x^3\)[/tex]: [tex]\(-4x^3\)[/tex] and [tex]\(-12x^3\)[/tex].
- One term with [tex]\(x^2\)[/tex]: [tex]\(9x^2\)[/tex].

2. Add the Coefficients for Like Terms:
- For the [tex]\(x^3\)[/tex] terms: [tex]\(-4x^3 - 12x^3\)[/tex] combines to [tex]\((-4 - 12)x^3 = -16x^3\)[/tex].

3. Write the Simplified Expression: Combine the simplified [tex]\(x^3\)[/tex] term with the [tex]\(x^2\)[/tex] term:
- This gives us [tex]\(-16x^3 + 9x^2\)[/tex].

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

Therefore, the correct choice from the given options is [tex]\(-16x^3 + 9x^2\)[/tex].