Factor completely: $x ^ { 3 } - 125 y ^ { 3 }$
A) $( x + 5 y ) ( x ^2 - 5 x y + 25 y ^2 )$
B) $( x - 5 y ) \left( x^ 2 + 5 x y + 25 y ^ { 2 } \right)$
C) $( x - 5 y ) ^ { 3 }$
D)$( x - 5 y ) ( x + 5 y ) ^ { 2 }$

Question

Factor completely: $x ^ { 3 } - 125 y ^ { 3 }$
A) $( x + 5 y ) ( x ^2 - 5 x y + 25 y ^2 )$ 
B) $( x - 5 y ) \left( x^ 2 + 5 x y + 25 y ^ { 2 } \right)$
C) $( x - 5 y ) ^ { 3 }$ 
D)$( x - 5 y ) ( x + 5 y ) ^ { 2 }$

Quizplus · Accepted Answer

This is a difference of cubes, which factors as $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$. Here, $a = x$ and $b = 5y$, so the correct factorization is $(x - 5y)(x^2 + 5xy + 25y^2)$.

Factor Completely x3−125y3x ^ { 3 } - 125 y ^ { 3 }x3−125y3

Factor Completely $x ^ { 3 } - 125 y ^ { 3 }$