Factor.
-$27 a ^ { 3 } - 125 b ^ { 3 }$
A) $( 3 a - 5 b ) \left( 9 a ^ { 2 } + 25 b ^ { 2 } \right)$
B) $( 3 a - 5 b ) \left( 9 a ^ { 2 } + 15 a b + 25 b ^ { 2 } \right)$
C) $( 27 a - 5 b ) \left( a ^ { 2 } + 15 a b + 25 b ^ { 2 } \right)$
D) $\left( 3 a + 5 b ^ { 2 } \right) \left( 9 a ^ { 2 } - 15 a b + 25 b ^ { 2 } \right)$

Question

Quizplus · Accepted Answer

This expression is a difference of cubes, which factors as $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$. Applying this formula with $a = 3a$ and $b = 5b$, we get $(3a - 5b)(9a^2 + 15ab + 25b^2)$.

Factor - 27a3−125b327 a ^ { 3 } - 125 b ^ { 3 }27a3−125b3

Factor
- $27 a ^ { 3 } - 125 b ^ { 3 }$