Factor by any method.
-$$10 a ^ { 3 } - 25 a ^ { 2 } b - 8 a b ^ { 2 } + 20 b ^ { 3 }$$
A) $\left( 5 a ^ { 2 } - 4 b \right) ( 2 a - 5 b )$
B) $\left( 5 a ^ { 2 } + 4 b ^ { 2 } \right) ( 2 a + 5 b )$
C) $\left( 10 a ^ { 2 } - 4 b ^ { 2 } \right) ( a - 5 b )$
D) $\left( 5 a ^ { 2 } - 4 b ^ { 2 } \right) ( 2 a - 5 b )$

Question

Quizplus · Accepted Answer

The given expression can be factored by grouping: $10a^3 - 25a^2b$ can be grouped together, and $-8ab^2 + 20b^3$ can be grouped together. Factoring out common factors from each group and then factoring by the difference of squares method leads to the correct answer, $\left( 5 a ^ { 2 } - 4 b ^ { 2 } \right) ( 2 a - 5 b )$.

Factor by Any Method 10a3−25a2b−8ab2+20b310 a ^ { 3 } - 25 a ^ { 2 } b - 8 a b ^ { 2 } + 20 b ^ { 3 }10a3−25a2b−8ab2+20b3

Factor by Any Method $10 a ^ { 3 } - 25 a ^ { 2 } b - 8 a b ^ { 2 } + 20 b ^ { 3 }$