Answer :
Certainly! Let's simplify the given expression step by step to find which of the options matches it:
The original expression is:
[tex]\[ -4x^3 - 12x^3 + 9x^2 \][/tex]
1. Combine Like Terms:
Start by combining the terms that have the same power of [tex]\( x \)[/tex]. Here, the terms [tex]\(-4x^3\)[/tex] and [tex]\(-12x^3\)[/tex] are like terms:
[tex]\[
-4x^3 - 12x^3 = -16x^3
\][/tex]
So the expression becomes:
[tex]\[
-16x^3 + 9x^2
\][/tex]
2. Factor the Expression:
Notice that both terms have a common factor of [tex]\( x^2 \)[/tex]. We can factor out [tex]\( x^2 \)[/tex] from the expression:
[tex]\[
-16x^3 + 9x^2 = x^2(-16x + 9)
\][/tex]
Thus, the expression simplifies to:
[tex]\[
x^2(9 - 16x)
\][/tex]
3. Match the Simplified Expression:
Our simplified expression is [tex]\( x^2(9 - 16x) \)[/tex]. If we compare it to the given choices, it matches the form of:
[tex]\[
-16x^3 + 9x^2
\][/tex]
So, the expression [tex]\(-16x^3 + 9x^2\)[/tex] is equivalent to the simplified version of the original expression. This is the correct choice.
The original expression is:
[tex]\[ -4x^3 - 12x^3 + 9x^2 \][/tex]
1. Combine Like Terms:
Start by combining the terms that have the same power of [tex]\( x \)[/tex]. Here, the terms [tex]\(-4x^3\)[/tex] and [tex]\(-12x^3\)[/tex] are like terms:
[tex]\[
-4x^3 - 12x^3 = -16x^3
\][/tex]
So the expression becomes:
[tex]\[
-16x^3 + 9x^2
\][/tex]
2. Factor the Expression:
Notice that both terms have a common factor of [tex]\( x^2 \)[/tex]. We can factor out [tex]\( x^2 \)[/tex] from the expression:
[tex]\[
-16x^3 + 9x^2 = x^2(-16x + 9)
\][/tex]
Thus, the expression simplifies to:
[tex]\[
x^2(9 - 16x)
\][/tex]
3. Match the Simplified Expression:
Our simplified expression is [tex]\( x^2(9 - 16x) \)[/tex]. If we compare it to the given choices, it matches the form of:
[tex]\[
-16x^3 + 9x^2
\][/tex]
So, the expression [tex]\(-16x^3 + 9x^2\)[/tex] is equivalent to the simplified version of the original expression. This is the correct choice.
