Perform the operation and simplify. $- 3 a ^ { 2 } ( a + 1 ) + 6 a \left( a ^ { 2 } - 4 \right) - a ^ { 2 } ( a + 10 )$
A) 0
B) $\quad 2 a ^ { 3 } - 13 a ^ { 2 } - 24$
C) $\quad 2 a ^ { 3 } - 13 a ^ { 2 } - 24 a$
D) $\quad 2 a ^ { 2 } + 13 a ^ { 4 } - 24$

Question

Quizplus · Accepted Answer

To simplify the expression, we use the distributive property and combine like terms:
$$
\begin{aligned} &-3a^2(a+1)+6a(a^2-4)-a^2(a+10) \
=& -3a^3-3a^2+6a^3-24a- a^3-10a^2 \
=& (2a^3-13a^2-24a)\
\end{aligned}
$$
So the answer is $\boxed{\textbf{(C)}}$.

Perform the Operation and Simplify −3a2(a+1)+6a(a2−4)−a2(a+10)- 3 a ^ { 2 } ( a + 1 ) + 6 a \left( a ^ { 2 } - 4 \right) - a ^ { 2 } ( a + 10 )−3a2(a+1)+6a(a2−4)−a2(a+10)

Perform the Operation and Simplify $- 3 a ^ { 2 } ( a + 1 ) + 6 a \left( a ^ { 2 } - 4 \right) - a ^ { 2 } ( a + 10 )$