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Answer :
Sure! Let's work through the expression step-by-step to find the equivalent expression.
We start with the expression:
[tex]\[ -4x^3 - 12x^3 + 9x^2 \][/tex]
1. Combine Like Terms:
Look for terms that have the same variable raised to the same power. In this case, [tex]\( -4x^3 \)[/tex] and [tex]\( -12x^3 \)[/tex] are like terms because they both involve [tex]\( x^3 \)[/tex].
2. Add the Coefficients of Like Terms:
[tex]\[
-4x^3 - 12x^3 = (-4 - 12)x^3 = -16x^3
\][/tex]
3. Write the Simplified Expression:
Now that we have combined the like terms, the expression simplifies to:
[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]
This matches with one of the provided options. If you have any more questions, feel free to ask!
We start with the expression:
[tex]\[ -4x^3 - 12x^3 + 9x^2 \][/tex]
1. Combine Like Terms:
Look for terms that have the same variable raised to the same power. In this case, [tex]\( -4x^3 \)[/tex] and [tex]\( -12x^3 \)[/tex] are like terms because they both involve [tex]\( x^3 \)[/tex].
2. Add the Coefficients of Like Terms:
[tex]\[
-4x^3 - 12x^3 = (-4 - 12)x^3 = -16x^3
\][/tex]
3. Write the Simplified Expression:
Now that we have combined the like terms, the expression simplifies to:
[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]
This matches with one of the provided options. If you have any more questions, feel free to ask!
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