Perform the operation and simplify. $- 3 a ^ { 2 } ( a + 1 ) + 7 a \left( a ^ { 2 } - 4 \right) - a ^ { 2 } ( a + 9 )$
A) $\quad 3 a ^ { 2 } + 12 a ^ { 4 } - 28$
B) $\quad 3 a ^ { 3 } - 12 a ^ { 2 } - 28$
C) 0
D) $\quad 3 a ^ { 3 } - 12 a ^ { 2 } - 28 a$

Question

Quizplus · Accepted Answer

First, distribute the coefficients:
\begin{align*}
-3a^3-3a^2 +7a^3-28a -a^3-9a^2&= (-3+7-1)a^3 + (-3-9)a^2 - 28a\
&= 3a^3-12a^2-28a
\end{align*}
Therefore, the correct answer is D.

Perform the Operation and Simplify −3a2(a+1)+7a(a2−4)−a2(a+9)- 3 a ^ { 2 } ( a + 1 ) + 7 a \left( a ^ { 2 } - 4 \right) - a ^ { 2 } ( a + 9 )−3a2(a+1)+7a(a2−4)−a2(a+9)

Perform the Operation and Simplify $- 3 a ^ { 2 } ( a + 1 ) + 7 a \left( a ^ { 2 } - 4 \right) - a ^ { 2 } ( a + 9 )$