QQuestionMathematics
QuestionMathematics
Which of the following expressions is equivalent to
$- 4 x^{3}- 12 x^{3}+ 9 x^{2} \boldsymbol{?}$
A. $x^{8}$
B. $- 7 x^{8}$
C. $- 8 x^{3}+ 9 x^{2}$
D. $- 16 x^{3}+ 9 x^{2}$
E. $- 16 x^{6}+ 9 x^{2}$
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Answer
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Step 1:: Combine like terms in the given expression.
-4x^{3}-12x^{3}+9x^{2} = -16x^{3}+9x^{2}
Step 2:: Analyze the resulting expression.
We can see that $a = 16$, $b = 3$, $c = 9$, and $d = 2$.
Step 3:: Compare the resulting expression with the answer choices.
We can eliminate options A and B because they have an $x^{8}$ term, which is not present in our expression.
Now, we have two options left: C and D.
Step 4:: Identify the correct answer.
Comparing the coefficients of $x^{3}$, we can see that our expression has a coefficient of -16, which matches option D.
Therefore, the correct answer is:
Final Answer
Comparing the coefficients of $x^{3}$, we can see that our expression has a coefficient of - 16, which matches option D.
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