Factor by grouping.
-$15 a ^ { 3 } + 9 a ^ { 2 } b + 25 a b ^ { 2 } + 15 b ^ { 3 }$
A) $\left( 15 a ^ { 2 } + 5 b ^ { 2 } \right) ( a + 3 b )$
B) $\left( 3 a ^ { 2 } - 5 b ^ { 2 } \right) ( 5 a - 3 b )$
C) $\left( 3 a ^ { 2 } + 5 b \right) ( 5 a + 3 b )$
D) $\left( 3 a ^ { 2 } + 5 b ^ { 2 } \right) ( 5 a + 3 b )$

Question

Quizplus · Accepted Answer

To factor by grouping, we first split the expression into two groups: $15a^3 + 9a^2b$ and $25ab^2 + 15b^3$. Factoring out the greatest common factor from each group gives us $3a^2(5a + 3b) + 5b^2(5a + 3b)$. Then, we can factor out the common factor $(5a + 3b)$, resulting in $(3a^2 + 5b^2)(5a + 3b)$, which matches choice D.

Factor by Grouping 15a3+9a2b+25ab2+15b315 a ^ { 3 } + 9 a ^ { 2 } b + 25 a b ^ { 2 } + 15 b ^ { 3 }15a3+9a2b+25ab2+15b3

Factor by Grouping $15 a ^ { 3 } + 9 a ^ { 2 } b + 25 a b ^ { 2 } + 15 b ^ { 3 }$