Factor out the greatest common factor. Simplify the factors, if possible.
-$10 a ^ { 3 } - 6 a ^ { 2 } b + 25 a b ^ { 2 } - 15 b ^ { 3 }$
A) $\left( 10 a ^ { 2 } + 5 b ^ { 2 } \right) ( a - 3 b )$
B) $\left( 2 a ^ { 2 } + 5 b \right) ( 5 a - 3 b )$
C) $\left( 2 a ^ { 2 } - 5 b ^ { 2 } \right) ( 5 a + 3 b )$
D) $\left( 2 a ^ { 2 } + 5 b ^ { 2 } \right) ( 5 a - 3 b )$

Question

Quizplus · Accepted Answer

The greatest common factor of the given expression is 1, so factoring involves grouping terms and factoring each group. Grouping $10a^3$ and $25ab^2$ together and $-6a^2b$ and $-15b^3$ together, we can factor out $5a$ from the first group and $-3b$ from the second group, leading to $5a(2a^2 + 5b^2) - 3b(2a^2 + 5b^2)$, which simplifies to $(2a^2 + 5b^2)(5a - 3b)$, matching option D.

Factor Out the Greatest Common Factor 10a3−6a2b+25ab2−15b310 a ^ { 3 } - 6 a ^ { 2 } b + 25 a b ^ { 2 } - 15 b ^ { 3 }10a3−6a2b+25ab2−15b3

Factor Out the Greatest Common Factor $10 a ^ { 3 } - 6 a ^ { 2 } b + 25 a b ^ { 2 } - 15 b ^ { 3 }$