Factor completely.
-$$128 x ^ { 3 } y - 250 y ^ { 4 }$$
A) $2 y ( 4 x - 5 y ) \left( 16 x ^ { 2 } + 20 x y + 25 y ^ { 2 } \right)$
B) $2 y \left( 4 x + 5 y ^ { 2 } \right) \left( 16 x ^ { 2 } - 20 x y + 25 x y ^ { 2 } \right)$
C) $2 y ( 64 x - 5 y ) \left( x ^ { 2 } + 20 x y + 25 y ^ { 2 } \right)$
D) $\left( 8 x y - 10 y ^ { 2 } \right) \left( 16 x ^ { 2 } + 25 y ^ { 2 } \right)$

Question

Quizplus · Accepted Answer

The greatest common factor of $128x^3y$ and $250y^4$ is $2y$, leaving us with $64x^3 - 125y^3$ inside the parentheses. This is a difference of cubes, which factors into $(4x - 5y)(16x^2 + 20xy + 25y^2)$.

Factor Completely 128x3y−250y4128 x ^ { 3 } y - 250 y ^ { 4 }128x3y−250y4

Factor Completely $128 x ^ { 3 } y - 250 y ^ { 4 }$