Which of the following expressions is equivalent to −4×3−12×3+9×2

Which of the following expressions is equivalent to −4×3−12×3+9×2?

​x8

−7×8

−8×3+9×2

−16×3+9×2

−16×6+9×2

The Correct Answer and Explanation is:

To find the equivalent expression to (-4x^3 – 12x^3 + 9x^2), we need to simplify the original expression by combining like terms.

Step-by-step Simplification:

1. Identify Like Terms:
   The expression consists of two types of terms:

• Terms involving (x^3): (-4x^3) and (-12x^3)
• A term involving (x^2): (9x^2)

1. Combine the Like Terms for (x^3):
   [
   -4x^3 – 12x^3 = (-4 – 12)x^3 = -16x^3
   ]
2. Combine with the (x^2) Term:
   Now, we can rewrite the expression:
   [
   -16x^3 + 9x^2
   ]

Conclusion:

Thus, the simplified expression is (-16x^3 + 9x^2).

Compare with the Options:

Now, let’s compare this result with the given options:

• (x^8)
• (-7x^8)
• (-8x^3 + 9x^2)
• (-16x^3 + 9x^2)
• (-16x^6 + 9x^2)

From our simplification, we can see that the expression (-16x^3 + 9x^2) matches one of the options exactly.

Final Answer:

Therefore, the equivalent expression to (-4x^3 – 12x^3 + 9x^2) is:
[
\boxed{-16x^3 + 9x^2}
]