Factor the polynomial by grouping.
-$8 a ^ { 3 } + 10 a ^ { 2 } b - 12 a b ^ { 2 } - 15 b ^ { 3 }$
A) $\left( 8 a ^ { 2 } - 3 b ^ { 2 } \right) ( a + 5 b )$
B) $\left( 2 a ^ { 2 } - 3 b \right) ( 4 a + 5 b )$
C) $\left( 2 a ^ { 2 } + 3 b ^ { 2 } \right) ( 4 a - 5 b )$
D) $\left( 2 a ^ { 2 } - 3 b ^ { 2 } \right) ( 4 a + 5 b )$

Question

Quizplus · Accepted Answer

First, group the polynomial as $8a^3 + 10a^2b$ and $-12ab^2 - 15b^3$. Factoring out the greatest common factor from each group gives $2a^2(4a + 5b) - 3b^2(4a + 5b)$. This can be further factored into $(2a^2 - 3b^2)(4a + 5b)$, which matches option D.

Factor the Polynomial by Grouping 8a3+10a2b−12ab2−15b38 a ^ { 3 } + 10 a ^ { 2 } b - 12 a b ^ { 2 } - 15 b ^ { 3 }8a3+10a2b−12ab2−15b3

Factor the Polynomial by Grouping $8 a ^ { 3 } + 10 a ^ { 2 } b - 12 a b ^ { 2 } - 15 b ^ { 3 }$