Perform the operation and simplify. $- 3 a ^ { 2 } ( a + 1 ) + 9 a \left( a ^ { 2 } - 6 \right) - a ^ { 2 } ( a + 6 )$
A) $\quad 5 a ^ { 3 } - 9 a ^ { 2 } - 54 a$
B) $\quad 5 a ^ { 3 } - 9 a ^ { 2 } - 54$
C) $\quad 5 a ^ { 2 } + 9 a ^ { 4 } - 54$
D) 0

Question

Quizplus · Accepted Answer

First, distribute the terms: $-3a^2(a + 1) = -3a^3 - 3a^2$, $9a(a^2 - 6) = 9a^3 - 54a$, and $-a^2(a + 6) = -a^3 - 6a^2$. Adding these together: $(-3a^3 + 9a^3 - a^3) + (-3a^2 - 6a^2) - 54a = 5a^3 - 9a^2 - 54a$.

Perform the Operation and Simplify −3a2(a+1)+9a(a2−6)−a2(a+6)- 3 a ^ { 2 } ( a + 1 ) + 9 a \left( a ^ { 2 } - 6 \right) - a ^ { 2 } ( a + 6 )−3a2(a+1)+9a(a2−6)−a2(a+6)

Perform the Operation and Simplify $- 3 a ^ { 2 } ( a + 1 ) + 9 a \left( a ^ { 2 } - 6 \right) - a ^ { 2 } ( a + 6 )$